The hydraulic elastic bulging roll system is a new roll system being developed in recent years.It is the first time in home that dead load test and study on this system has been made.Based on the experiment,the analys...The hydraulic elastic bulging roll system is a new roll system being developed in recent years.It is the first time in home that dead load test and study on this system has been made.Based on the experiment,the analysis solution of the bulging convexity of the hydraulic elastic bulging roll was obtained by selecting appropriate displacement function and adopting inverse solution of the elasticity theory.In evaluating,a variable displacement function and its solving method was advanced.The analysis results are in accord with the experiment's.Some conclusions have laid the foundation of establishing close-loop controlled mathematical model of the hydraulic elastic bulging roll system.展开更多
The fluorescence spectrum of the ether-water solution excited by the ultraviolet light with the wavelength of 245 nm is experimentally detected. Based on the second derivative analysis, the fluorescence spectrum of th...The fluorescence spectrum of the ether-water solution excited by the ultraviolet light with the wavelength of 245 nm is experimentally detected. Based on the second derivative analysis, the fluorescence spectrum of the ether-water solution is used as Gaussian decomposition and seven Gaussian spectral lines are obtained. The center wavelength, the peak intensity and the half peak bandwidth of each Gaussian spectral line are measured, and the multi-peak fitting is made by using Gaussian primitive parameters. The highest and the lowest oscillation energy level differences in the ground state of each Gaussian spectrum are calculated. It is found that there are seven types of luminescent association molecules formed by ether and water molecules in different configurations existed in the solution. The location of each optimum absorption wavelength and the half peak bandwidth of the Gaussian spectral line is different. The energy level difference with the central wavelength of 304 nm attains the maximum value The result can contribute to the study of the molecular association in ether-water solution.展开更多
By means of the modified Clarkson and Kruskal (CK) direct method and the variable separation approach, we investigate the (24-1)-dimensional Ito equation which was constructed by Ito in 1980. The full symmetry gro...By means of the modified Clarkson and Kruskal (CK) direct method and the variable separation approach, we investigate the (24-1)-dimensional Ito equation which was constructed by Ito in 1980. The full symmetry group with the Kac-Moody-Virasoro algebra structure and the variable separation solutions are obtained. By selecting appropriate arbitrary functions, some special soliton excitations are shown graphically. The results presented here would be beneficial for understanding the (2-t-1)-dimensional Ito equation better.展开更多
This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of pla...This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and condi- tions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approxi- mate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate so- lutions. It can be seen that the error is infinitesimal decreasing in the exponential form.展开更多
Using theoretical analysis, the single-phase gas seepage mathematical model influenced by slippage effects was established. The results show that the pressure of producing wells attenuates more violently than the well...Using theoretical analysis, the single-phase gas seepage mathematical model influenced by slippage effects was established. The results show that the pressure of producing wells attenuates more violently than the wells without slippage effects. The decay rate of reservoir pressure is more violent as the Klinkenherg factor increases. The gas prediction output gradually increases as the Klinenberg factor increases when considering gas slippage effects. Through specific examples, analyzed the law of stope pore pressure and gas output forecast changing in a hypotonic reservoir with slippage effects. The results have great theoretical significance in the study of the law of coal-bed methane migration in hypotonic reservoirs and for the exploitation of coal-bed methane.展开更多
The transport of fluid, nutrients, and signaling molecules in the bone lacunar-canalicular system (LCS) is critical for osteocyte survival and function. We have applied the fluorescence recovery after photobleaching...The transport of fluid, nutrients, and signaling molecules in the bone lacunar-canalicular system (LCS) is critical for osteocyte survival and function. We have applied the fluorescence recovery after photobleaching (FRAP) approach to quantify load-induced fluid and solute transport in the LCS in situ, but the measurements were limited to cortical regions 30-50 μm underneath the periosteum due to the constrains of laser penetration. With this work, we aimed to expand our understanding of load-induced fluid and solute transport in both trabecular and cortical bone using a multiscaled image-based finite element analysis (FEA) approach. An intact murine tibia was first re-constructed from microCT images into a three-dimensional (3D) linear elastic FEA model, and the matrix deformations at various locations were calculated under axial loading. A segment of the above 3D model was then imported to the biphasic poroelasticity analysis platform (FEBio) to predict load-induced fluid pressure fields, and interstitial solute/fluid flows through LCS in both cortical and trabecular regions. Further, secondary flow effects such as the shear stress and/or drag force acting on osteocytes, the presumed mechano-sensors in bone, were derived using the previously developed ultrastructural model of Brinkman flow in the canaliculi. The material properties assumed in the FEA models were validated against previously obtained strain and FRAP transport data measured on the cortical cortex. Our results demonstrated the feasibility of this computational approach in estimating the fluid flux in the LCS and the cellular stimulation forces (shear and drag forces) for osteocytes in any cortical and trabecular bone locations, allowing further studies of how the activation of osteocytes correlates with in vivo functional bone formation. The study provides a promising platform to reveal potential cellular mechanisms underlying the anabolic power of exercises and physical activities in treating patients with skeletal deficiencies.展开更多
Several action regimes were employed, namely, those exposed to solutions containing single and/or composite chloride and sulfate salts, and under wet-dry cycles and/or flexural loading. The variations in dynamic modul...Several action regimes were employed, namely, those exposed to solutions containing single and/or composite chloride and sulfate salts, and under wet-dry cycles and/or flexural loading. The variations in dynamic modulus of elasticity(Erd values) were monitored, as well as the key factor impacting on the chloride ingress when concrete subjected to multiple action regimes was identified by the method of Grey Relation Analysis(GRA). The changes in micro-structures and mineral products of interior concrete after different action regimes were investigated by means of X-ray diffraction(XRD), mercury intrusion technique(MIP), and scanning electron microscopy(SEM). The test results showed that the cyclic wet-dry accelerated the deterioration of OPC concrete more than the action of 35% flexural loading based on the results of Erd values and the GEA. The analyses from micro-structures could give certain explanations to the change in Erd values under different action regimes.展开更多
An approximate analytical model for calculating the pull-in voltage of a stepped cantilever-type radio frequency (RF) micro electro-mechanical system (MEMS) switch is developed based on the Euler-Bernoulli beam an...An approximate analytical model for calculating the pull-in voltage of a stepped cantilever-type radio frequency (RF) micro electro-mechanical system (MEMS) switch is developed based on the Euler-Bernoulli beam and a modified couple stress theory, and is validated by comparison with the finite element results. The sensitivity functions of the pull-in voltage to the designed parameters are derived based on the proposed model. The sensitivity investigation shows that the pull-in voltage sensitivities increase/decrease nonlinearly with the increases in the designed parameters. For the stepped cantilever beam, there exists a nonzero optimal dimensionless length ratio, where the pull-in voltage is insensitive. The optimal value of the dimensionless length ratio only depends on the dimensionless width ratio, and can be obtained by solving a nonlinear equation. The determination of the designed parameters is discussed, and some recommendations are made for the RF MEMS switch optimization.展开更多
This investigation examines the time dependent magnetohydrodynamic (MHD) flow problem of a micropolar fluid between two radially stretching sheets. Both strong and weak concentrations of microelements are taken into...This investigation examines the time dependent magnetohydrodynamic (MHD) flow problem of a micropolar fluid between two radially stretching sheets. Both strong and weak concentrations of microelements are taken into account. Suitable transformations are employed for the conversion of partial differential equations into ordinary differential equations. Solutions to the resulting problems are developed with a homotopy analysis method (HAM). The angular velocity, skin friction coefficient, and wall couple stress coefficient are illustrated for various parameters.展开更多
With the purpose of improving the ability of students' listening comprehension and the quality of listening, by means of questionnaire and listening test, based on the analysis of statistics, this paper suggests ling...With the purpose of improving the ability of students' listening comprehension and the quality of listening, by means of questionnaire and listening test, based on the analysis of statistics, this paper suggests linguistic knowledge, listening material, skills, techniques and strategy of listening, psychological factors and cultural and background knowledge are the possible factors that affect listening comprehension, meanwhile they provide respective solutions.展开更多
According to the defect of traditional method of determining instantaneous contact regions for conjugate surfaces, a numerical approach to the determination is proposed. A local coordinate system is built by using the...According to the defect of traditional method of determining instantaneous contact regions for conjugate surfaces, a numerical approach to the determination is proposed. A local coordinate system is built by using the surface unit tangent and unit normal at the contact point. Considering that the gap forming the boundary of instantaneous contact region in the direction of the common normal vectors is given, a system of nonlinear equations is built to find the instantaneous contact boundary in local coordinate system, a modified Powell's hybrid algorithm of finite-difference approximation to the Jacobian used to solve the system. The new method simplifies the task of determining instantaneous contact regions without calculating curvatm'e and relative curvature. The validity of the proposed approach is verified by an example of hypoid gears.展开更多
Micro-hotplate (MHP) technology is one key part in the manufacturing of gas sensors. The pursuit of analytical solutions for the temperature distribution and also thermal stresses within the MHP is of intrinsic scie...Micro-hotplate (MHP) technology is one key part in the manufacturing of gas sensors. The pursuit of analytical solutions for the temperature distribution and also thermal stresses within the MHP is of intrinsic scientific interest. In this study, analytical solutions for the temperature field, and both radial and tangential stresses and van Mises stress for circular MHP were obtained. Two geometries were considered: one had a circular heater at the center and the other had a circular heater at the center and an annular heater within the membrane part. Internal heat generation was incorporated in the energy equation for the MHP and different values of convection heat transfer coefficient were used at the upper and lower surfaces of the MHP. It has been shown that the MHP with two heaters can provide more uniform temperature field compared with the MHP with one heater. The main objective of this work is to provide an exact analytical solution for thermal stresses within the circular micro-hcater with a simple geometry as a benchmark, from mathematical point of view, against which the accuracy of new numerical schemes can be checked. To make sure that the analytical procedure is correct, the analytical results are checked against numerical solutions derived from finite element simulation. Since the analytical models for the temperature field and especially for the thermal stresses of MHP ace seldom investigated in the literature, the obtained results are believed to facilitate the design and performance evaluation of MHPs as well.展开更多
The spoofing capability of Global Navigation Satellite System(GNSS)represents an important confrontational capability for navigation security,and the success of planned missions may depend on the effective evaluation ...The spoofing capability of Global Navigation Satellite System(GNSS)represents an important confrontational capability for navigation security,and the success of planned missions may depend on the effective evaluation of spoofing capability.However,current evaluation systems face challenges arising from the irrationality of previous weighting methods,inapplicability of the conventional multi-attribute decision-making method and uncertainty existing in evaluation.To solve these difficulties,considering the validity of the obtained results,an evaluation method based on the game aggregated weight model and a joint approach involving the grey relational analysis and technique for order preference by similarity to an ideal solution(GRA-TOPSIS)are firstly proposed to determine the optimal scheme.Static and dynamic evaluation results under different schemes are then obtained via a fuzzy comprehensive assessment and an improved dynamic game method,to prioritize the deceptive efficacy of the equipment accurately and make pointed improvement for its core performance.The use of judging indicators,including Spearman rank correlation coefficient and so on,combined with obtained evaluation results,demonstrates the superiority of the proposed method and the optimal scheme by the horizontal comparison of different methods and vertical comparison of evaluation results.Finally,the results of field measurements and simulation tests show that the proposed method can better overcome the difficulties of existing methods and realize the effective evaluation.展开更多
The extended form of modified Kadomtsev–Petviashvili equation with variable-coefficient is investigated in the framework of Painlevé analysis. The Lax pairs are obtained by analysing two Painlevé branches o...The extended form of modified Kadomtsev–Petviashvili equation with variable-coefficient is investigated in the framework of Painlevé analysis. The Lax pairs are obtained by analysing two Painlevé branches of this equation.Starting with the Lax pair, the N-times Darboux transformation is constructed and the N-soliton solution formula is given, which contains 2n free parameters and two arbitrary functions. Furthermore, with different combinations of the parameters, several types of soliton solutions are calculated from the first order to the third order. The regularity conditions are discussed in order to avoid the singularity of the solutions. Moreover, we construct the generalized Darboux transformation matrix by considering a special limiting process and find a rational-type solution for this equation.展开更多
文摘The hydraulic elastic bulging roll system is a new roll system being developed in recent years.It is the first time in home that dead load test and study on this system has been made.Based on the experiment,the analysis solution of the bulging convexity of the hydraulic elastic bulging roll was obtained by selecting appropriate displacement function and adopting inverse solution of the elasticity theory.In evaluating,a variable displacement function and its solving method was advanced.The analysis results are in accord with the experiment's.Some conclusions have laid the foundation of establishing close-loop controlled mathematical model of the hydraulic elastic bulging roll system.
基金Supported by the Natural Science Foundation of Jiangsu Province(BK2007204)the Natural Sci-ence Foundation of Educational Department of Jiangsu Province(07KJD140208)~~
文摘The fluorescence spectrum of the ether-water solution excited by the ultraviolet light with the wavelength of 245 nm is experimentally detected. Based on the second derivative analysis, the fluorescence spectrum of the ether-water solution is used as Gaussian decomposition and seven Gaussian spectral lines are obtained. The center wavelength, the peak intensity and the half peak bandwidth of each Gaussian spectral line are measured, and the multi-peak fitting is made by using Gaussian primitive parameters. The highest and the lowest oscillation energy level differences in the ground state of each Gaussian spectrum are calculated. It is found that there are seven types of luminescent association molecules formed by ether and water molecules in different configurations existed in the solution. The location of each optimum absorption wavelength and the half peak bandwidth of the Gaussian spectral line is different. The energy level difference with the central wavelength of 304 nm attains the maximum value The result can contribute to the study of the molecular association in ether-water solution.
基金Supported by the Zhejiang Provincial Natural Science Foundation of China under Grant No LQ13A010014the National Natural Science Foundation of China under Grant Nos 11326164,11401528,11435005 and 11375090+4 种基金the Global Change Research Program of China(No 2015CB953904)the Research Fund for the Doctoral Program of Higher Education of China(No 20120076110024)the Network Information Physics Calculation of Basic Research Innovation Research Group of China under Grant No 61321064Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things(No ZF1213)Shanghai Minhang District Talents of High Level Scientific Research Project
文摘By means of the modified Clarkson and Kruskal (CK) direct method and the variable separation approach, we investigate the (24-1)-dimensional Ito equation which was constructed by Ito in 1980. The full symmetry group with the Kac-Moody-Virasoro algebra structure and the variable separation solutions are obtained. By selecting appropriate arbitrary functions, some special soliton excitations are shown graphically. The results presented here would be beneficial for understanding the (2-t-1)-dimensional Ito equation better.
基金Project supported by the National Natural Science Foundation of China(No.11071164)the Innovation Program of Shanghai Municipal Education Commission(No.13ZZ118)+1 种基金the Shanghai Leading Academic Discipline Project(No.XTKX2012)the Innovation Fund Project for Graduate Stu-dent of Shanghai(No.JWCXSL1201)
文摘This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and condi- tions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approxi- mate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate so- lutions. It can be seen that the error is infinitesimal decreasing in the exponential form.
基金Supported by the Youth Program of the National Natural Science Foundation of China (51004061)
文摘Using theoretical analysis, the single-phase gas seepage mathematical model influenced by slippage effects was established. The results show that the pressure of producing wells attenuates more violently than the wells without slippage effects. The decay rate of reservoir pressure is more violent as the Klinkenherg factor increases. The gas prediction output gradually increases as the Klinenberg factor increases when considering gas slippage effects. Through specific examples, analyzed the law of stope pore pressure and gas output forecast changing in a hypotonic reservoir with slippage effects. The results have great theoretical significance in the study of the law of coal-bed methane migration in hypotonic reservoirs and for the exploitation of coal-bed methane.
基金supported by grants from NIH (P30GM103333 and RO1AR054385 to LW)China CSC fellowship (to LF)DOD W81XWH-13-1-0148 (to XLL)
文摘The transport of fluid, nutrients, and signaling molecules in the bone lacunar-canalicular system (LCS) is critical for osteocyte survival and function. We have applied the fluorescence recovery after photobleaching (FRAP) approach to quantify load-induced fluid and solute transport in the LCS in situ, but the measurements were limited to cortical regions 30-50 μm underneath the periosteum due to the constrains of laser penetration. With this work, we aimed to expand our understanding of load-induced fluid and solute transport in both trabecular and cortical bone using a multiscaled image-based finite element analysis (FEA) approach. An intact murine tibia was first re-constructed from microCT images into a three-dimensional (3D) linear elastic FEA model, and the matrix deformations at various locations were calculated under axial loading. A segment of the above 3D model was then imported to the biphasic poroelasticity analysis platform (FEBio) to predict load-induced fluid pressure fields, and interstitial solute/fluid flows through LCS in both cortical and trabecular regions. Further, secondary flow effects such as the shear stress and/or drag force acting on osteocytes, the presumed mechano-sensors in bone, were derived using the previously developed ultrastructural model of Brinkman flow in the canaliculi. The material properties assumed in the FEA models were validated against previously obtained strain and FRAP transport data measured on the cortical cortex. Our results demonstrated the feasibility of this computational approach in estimating the fluid flux in the LCS and the cellular stimulation forces (shear and drag forces) for osteocytes in any cortical and trabecular bone locations, allowing further studies of how the activation of osteocytes correlates with in vivo functional bone formation. The study provides a promising platform to reveal potential cellular mechanisms underlying the anabolic power of exercises and physical activities in treating patients with skeletal deficiencies.
基金Funded by the National Natural Science Foundation of China(51578141)the Major State Basic Research Development Program of China(973 Program)(2015CB655102)+1 种基金the Program Most of China(2016YFE0118200)the support of China Scholarship Council
文摘Several action regimes were employed, namely, those exposed to solutions containing single and/or composite chloride and sulfate salts, and under wet-dry cycles and/or flexural loading. The variations in dynamic modulus of elasticity(Erd values) were monitored, as well as the key factor impacting on the chloride ingress when concrete subjected to multiple action regimes was identified by the method of Grey Relation Analysis(GRA). The changes in micro-structures and mineral products of interior concrete after different action regimes were investigated by means of X-ray diffraction(XRD), mercury intrusion technique(MIP), and scanning electron microscopy(SEM). The test results showed that the cyclic wet-dry accelerated the deterioration of OPC concrete more than the action of 35% flexural loading based on the results of Erd values and the GEA. The analyses from micro-structures could give certain explanations to the change in Erd values under different action regimes.
基金supported by the National Natural Science Foundation of China(Nos.51505089 and61204116)the Opening Project of the Science and Technology on Reliability Physics and Application Technology of Electronic Component Laboratory(Nos.ZHD201207 and 9140C030605140C03015)the Pearl River S&T Nova Program of Guangzhou(No.2014J2200086)
文摘An approximate analytical model for calculating the pull-in voltage of a stepped cantilever-type radio frequency (RF) micro electro-mechanical system (MEMS) switch is developed based on the Euler-Bernoulli beam and a modified couple stress theory, and is validated by comparison with the finite element results. The sensitivity functions of the pull-in voltage to the designed parameters are derived based on the proposed model. The sensitivity investigation shows that the pull-in voltage sensitivities increase/decrease nonlinearly with the increases in the designed parameters. For the stepped cantilever beam, there exists a nonzero optimal dimensionless length ratio, where the pull-in voltage is insensitive. The optimal value of the dimensionless length ratio only depends on the dimensionless width ratio, and can be obtained by solving a nonlinear equation. The determination of the designed parameters is discussed, and some recommendations are made for the RF MEMS switch optimization.
文摘This investigation examines the time dependent magnetohydrodynamic (MHD) flow problem of a micropolar fluid between two radially stretching sheets. Both strong and weak concentrations of microelements are taken into account. Suitable transformations are employed for the conversion of partial differential equations into ordinary differential equations. Solutions to the resulting problems are developed with a homotopy analysis method (HAM). The angular velocity, skin friction coefficient, and wall couple stress coefficient are illustrated for various parameters.
文摘With the purpose of improving the ability of students' listening comprehension and the quality of listening, by means of questionnaire and listening test, based on the analysis of statistics, this paper suggests linguistic knowledge, listening material, skills, techniques and strategy of listening, psychological factors and cultural and background knowledge are the possible factors that affect listening comprehension, meanwhile they provide respective solutions.
基金National Education Dep.of China (No. 20060056016)National Hi-tech Research and Development Program of China(863 Program, No. 2007AA042005, No. 2006AA 04Z146).
文摘According to the defect of traditional method of determining instantaneous contact regions for conjugate surfaces, a numerical approach to the determination is proposed. A local coordinate system is built by using the surface unit tangent and unit normal at the contact point. Considering that the gap forming the boundary of instantaneous contact region in the direction of the common normal vectors is given, a system of nonlinear equations is built to find the instantaneous contact boundary in local coordinate system, a modified Powell's hybrid algorithm of finite-difference approximation to the Jacobian used to solve the system. The new method simplifies the task of determining instantaneous contact regions without calculating curvatm'e and relative curvature. The validity of the proposed approach is verified by an example of hypoid gears.
文摘Micro-hotplate (MHP) technology is one key part in the manufacturing of gas sensors. The pursuit of analytical solutions for the temperature distribution and also thermal stresses within the MHP is of intrinsic scientific interest. In this study, analytical solutions for the temperature field, and both radial and tangential stresses and van Mises stress for circular MHP were obtained. Two geometries were considered: one had a circular heater at the center and the other had a circular heater at the center and an annular heater within the membrane part. Internal heat generation was incorporated in the energy equation for the MHP and different values of convection heat transfer coefficient were used at the upper and lower surfaces of the MHP. It has been shown that the MHP with two heaters can provide more uniform temperature field compared with the MHP with one heater. The main objective of this work is to provide an exact analytical solution for thermal stresses within the circular micro-hcater with a simple geometry as a benchmark, from mathematical point of view, against which the accuracy of new numerical schemes can be checked. To make sure that the analytical procedure is correct, the analytical results are checked against numerical solutions derived from finite element simulation. Since the analytical models for the temperature field and especially for the thermal stresses of MHP ace seldom investigated in the literature, the obtained results are believed to facilitate the design and performance evaluation of MHPs as well.
基金supported by the National Natural Science Foundation of China(41804035,41374027)。
文摘The spoofing capability of Global Navigation Satellite System(GNSS)represents an important confrontational capability for navigation security,and the success of planned missions may depend on the effective evaluation of spoofing capability.However,current evaluation systems face challenges arising from the irrationality of previous weighting methods,inapplicability of the conventional multi-attribute decision-making method and uncertainty existing in evaluation.To solve these difficulties,considering the validity of the obtained results,an evaluation method based on the game aggregated weight model and a joint approach involving the grey relational analysis and technique for order preference by similarity to an ideal solution(GRA-TOPSIS)are firstly proposed to determine the optimal scheme.Static and dynamic evaluation results under different schemes are then obtained via a fuzzy comprehensive assessment and an improved dynamic game method,to prioritize the deceptive efficacy of the equipment accurately and make pointed improvement for its core performance.The use of judging indicators,including Spearman rank correlation coefficient and so on,combined with obtained evaluation results,demonstrates the superiority of the proposed method and the optimal scheme by the horizontal comparison of different methods and vertical comparison of evaluation results.Finally,the results of field measurements and simulation tests show that the proposed method can better overcome the difficulties of existing methods and realize the effective evaluation.
基金Supported by the Global Change Research Program of China under Grant No.2015CB953904National Natural Science Foundation of China under Grant Nos.11275072 and 11435005+3 种基金Doctoral Program of Higher Education of China under Grant No.20120076110024The Network Information Physics Calculation of basic research innovation research group of China under Grant No.61321064Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No.ZF1213Shanghai Minhang District talents of high level scientific research project
文摘The extended form of modified Kadomtsev–Petviashvili equation with variable-coefficient is investigated in the framework of Painlevé analysis. The Lax pairs are obtained by analysing two Painlevé branches of this equation.Starting with the Lax pair, the N-times Darboux transformation is constructed and the N-soliton solution formula is given, which contains 2n free parameters and two arbitrary functions. Furthermore, with different combinations of the parameters, several types of soliton solutions are calculated from the first order to the third order. The regularity conditions are discussed in order to avoid the singularity of the solutions. Moreover, we construct the generalized Darboux transformation matrix by considering a special limiting process and find a rational-type solution for this equation.