The cubic-quintic nonlinear Schroedinger equation (CQNLS) plays important parts in the optical fiber and the nuclear hydrodynamics. By using the homogeneous balance principle, the bell type, kink type, algebraic sol...The cubic-quintic nonlinear Schroedinger equation (CQNLS) plays important parts in the optical fiber and the nuclear hydrodynamics. By using the homogeneous balance principle, the bell type, kink type, algebraic solitary waves, and trigonometric traveling waves for the cubic-quintic nonlinear Schroedinger equation with variable coefficients (vCQNLS) are derived with the aid of a set of subsidiary high-order ordinary differential equations (sub-equations for short). The method used in this paper might help one to derive the exact solutions for the other high-order nonlinear evolution equations, and shows the new application of the homogeneous balance principle.展开更多
A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for (3+1)-dimensional Kadomtsev-Petviashvilli (KP) equation. Among them, th...A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for (3+1)-dimensional Kadomtsev-Petviashvilli (KP) equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions.展开更多
In this paper, we put our focus on a variable-coe^cient fifth-order Korteweg-de Vries (fKdV) equation, which possesses a great number of excellent properties and is of current importance in physical and engineering ...In this paper, we put our focus on a variable-coe^cient fifth-order Korteweg-de Vries (fKdV) equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those constraints, some integrable properties are derived, such as the Lax pair and Darboux transformation. Via the Darboux transformation, which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out.展开更多
By using the homogeneous balance principle(HBP), we derive a Backtund transformation(BT) to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact...By using the homogeneous balance principle(HBP), we derive a Backtund transformation(BT) to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact solutions of the equation, such as, singlesolitary solutions, multi-soliton solutions and generalized exact solutions.展开更多
In this paper, we derive the bilinear form for a variable-coefficient Kadomtsev Petviashvili-typed equation. Based on the bilinear form, we obtain the Wronskian determinant solution, which is proved to be indeed an ex...In this paper, we derive the bilinear form for a variable-coefficient Kadomtsev Petviashvili-typed equation. Based on the bilinear form, we obtain the Wronskian determinant solution, which is proved to be indeed an exact solution of this equation through the Wronskian technique. In addition, we testify that this equation can be reduced to a Jacobi identity by considering its solution as a Grammian determinant by means of Pfaffian derivative formulae.展开更多
By the symbolic computation and Hirota method, the bilinear form and an auto-Backlund transformation for a variable-coemcient Korteweg-de Vries equation with nonuniformities are given. Then, the N-solitonic solution i...By the symbolic computation and Hirota method, the bilinear form and an auto-Backlund transformation for a variable-coemcient Korteweg-de Vries equation with nonuniformities are given. Then, the N-solitonic solution in terms of Wronskian form is obtained and verified. In addition, it is shown that the (N - 1)- and N-solitonic solutions satisfy the auto-Backlund transformation through the Wronskian technique.展开更多
We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponent...We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.展开更多
In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the (2+1)-dimensional variable coefficients Broer-Kaup (VCBK) equations. The...In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the (2+1)-dimensional variable coefficients Broer-Kaup (VCBK) equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.展开更多
In this paper, we extend the mapping transformation method through introducing variable coefficients.By means of the extended mapping transformation method, many explicit and exact general solutions with arbitrary fun...In this paper, we extend the mapping transformation method through introducing variable coefficients.By means of the extended mapping transformation method, many explicit and exact general solutions with arbitrary functions for some nonlinear partial differential equations, which contain solitary wave solutions, trigonometric function solutions, and rational solutions, are obtained.展开更多
The vector susceptibility is investigated numerically in the Dyson-Schwinger approach. The results agree with those obtained analytically previously by using a simple gluon propagator.
Abstract Selection of net with a suitable mesh size is a key concern in the quantitative assessment of zooplankton, which is cru- cial to understand pelagic ecosystem processes. This study compared the copepod collect...Abstract Selection of net with a suitable mesh size is a key concern in the quantitative assessment of zooplankton, which is cru- cial to understand pelagic ecosystem processes. This study compared the copepod collecting efficiency of three commonly used plankton nets, namely, the China standard coarse net (505 gm mesh), the China standard fine net (77 gin), and the WP-2 net (200 μm) The experiment was performed at six stations in the Bohai Sea during the autumn of 2012. The coarse net substantially un- der-sampled small individuals (body widths 〈 672 gm) and led to the lowest species number in each tow, whereas the fine net col- lected all small copepod species but failed to collect rare species. The WP-2 net appeared to be a compromise of the two other nets, collecting both small copepods and rare species. The abundance of copepods collected by the coarse net (126.4±86.5 indm-3) was one to two orders of magnitude lower than that by the WP-2 net (5802.4 ± 2595.4 indm3), and the value of the fine net (11117.0±4563.41 indm-3) was nearly twice that of the WP-2 net. The abundance of large copepods (i.e., adult Calanus sinicus) in the three nets showed no significant differences, but the abundance of small copepods declined with decreasing mesh size. The dif- ference in abundance resulted from the under-sampling of small copepods with body widths 〈 672 μm and 〈 266μm by the coarse and WP-2 nets, respectively.展开更多
In this paper, the generalized ranch function method is extended to (2+1)-dimensianal canonical generalized KP (CGKP) equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit ...In this paper, the generalized ranch function method is extended to (2+1)-dimensianal canonical generalized KP (CGKP) equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit exact solutions, which contain multiple soliton-like and periodic solutions, are obtained for the (2+1)-dimensional OGKP equation with variable coetffcients.展开更多
Abstract: A joint solution model of variabk:-mass flow in two-phase region and fluid-solid coupling heat transfer, concerned about the charge process of variable-mass thermodynamic system, is built up and calculated...Abstract: A joint solution model of variabk:-mass flow in two-phase region and fluid-solid coupling heat transfer, concerned about the charge process of variable-mass thermodynamic system, is built up and calculated by the finite element method (FEM). The results are basically consistent with relative experimental data. The calculated average heat transfer coefficient reaches 1.7~105 W/(m2. K). When the equal percentage valve is used, the system needs the minimum requirements of valve control, but brings the highest construction cost. With the: decrease of initial steam pressure, the heat transfer intensity also weakens but the steam flow increases. With the initial water filling coefficient increasing or the temperature of steam supply decreasing, the amount of accumulative steam flow increases with the growth of steam pressure. When the pressure of steam supply drops, the steam flow gradient increases during the maximum opening period of control valve, and causes the maximum steam flow to increase.展开更多
Based on existing low-frequency water-filled impedance tube testing facilities, which is a part of the Low Frequency Facility of the Naval Undersea Warfare Center in Beijing, an improved water-filled pulse tube method...Based on existing low-frequency water-filled impedance tube testing facilities, which is a part of the Low Frequency Facility of the Naval Undersea Warfare Center in Beijing, an improved water-filled pulse tube method is presented in this short paper. This proposed study is significantly different from the conventional pulse tube method because of the capability for a single plane damped sine pulse wave to generate in the water-filled pulse tube with a regular waveform and short duration time of about 1ms. During the generation process of the pulse, an inverse filter principle was adopted to compensate the transducer response. The effect of the characteristics of tube termination can be eliminated through the generation process of the pulse. Reflection coefficient from a water/air interface was measured to verify the proposed method. When compared with the expected theoretical values, a relatively good agreement can be obtained in the low frequency range of 500-2 000 Hz.展开更多
Based on the energy equation of gas-liquid flow in pipeline,the explicit temperature drop formula for gas-liquid steady state calculation was derived.This formula took into consideration the Joule-Thomson effect,impac...Based on the energy equation of gas-liquid flow in pipeline,the explicit temperature drop formula for gas-liquid steady state calculation was derived.This formula took into consideration the Joule-Thomson effect,impact of terrain undulation and heat transfer with the surroundings along the line.Elimination of temperature iteration loop and integration of the explicit temperature equation,instead of enthalpy energy equation,into the conjugated hydraulic and thermal computation have been found to improve the efficiency of algorithm.Then,the inner wall temperature of gas-liquid flow was calculated by using explicit temperature equation and inner wall convective heat transfer coefficient of mixed flow which can be obtained by liquid convective heat transfer coefficient and gas convective heat transfer coefficient on the basis of liquid holdup.The temperature results of gas-liquid flow and inner wall in the case example presented both agree well with those in professional multiphase computational software OLGA.展开更多
We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue a...We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for such a system are given, they have the same forms as those for the usual harmonic oscillator with constant mass. The coherent state and its properties corresponding effective potentials for several mass functions, for the system with PDM are also discussed. We give the the systems with such potentials are isospectral to the usual harmonic oscillator.展开更多
In this paper, a novel reconstruction technique based on level set method and algebraic reconstruction technique is proposed for multiphase flow computed tomography (CT) system. The curvature-driven noise reduction me...In this paper, a novel reconstruction technique based on level set method and algebraic reconstruction technique is proposed for multiphase flow computed tomography (CT) system. The curvature-driven noise reduction method is inserted into the conventional iteration procedure of algebraic reconstruction technique to improve the image quality and convergence speed with limited projection data. By evolving the image as a set of iso-intensity contours after each updation, the sufficient number of iterations for acceptable results is reduced by 80%-90%, while the image quality is enhanced obviously. Quantitative evaluation of image quality is given by using both relative image error and correlation coefficient. The resultant images can be utilized to detect flow regimes for monitoring industrial multiphase flow. Laboratory results demonstrate the feasibility of the proposed method. Phantoms of four typical flow regimes can be reconstructed from few-view projection data efficiently, and the corresponding image errors and correlation coefficients are acceptable for the cases tested in this paper.展开更多
基金The project supported in part by Natural Science Foundation of Henan Province of China under Grant No. 2006110002 and the Science Foundation of Henan University of Science and Technology under Grant No. 2004ZD002
文摘The cubic-quintic nonlinear Schroedinger equation (CQNLS) plays important parts in the optical fiber and the nuclear hydrodynamics. By using the homogeneous balance principle, the bell type, kink type, algebraic solitary waves, and trigonometric traveling waves for the cubic-quintic nonlinear Schroedinger equation with variable coefficients (vCQNLS) are derived with the aid of a set of subsidiary high-order ordinary differential equations (sub-equations for short). The method used in this paper might help one to derive the exact solutions for the other high-order nonlinear evolution equations, and shows the new application of the homogeneous balance principle.
文摘A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for (3+1)-dimensional Kadomtsev-Petviashvilli (KP) equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions.
基金The project supported by the Key Project of the Chinese Ministry of Education under Grant No.106033the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20060006024+2 种基金Chinese Ministry of Education,the National Natural Science Foundation of China under Grant Nos.60772023 and 60372095the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.SKLSDE-07-001Beijing University of Aeronautics and Astronautics,and by the National Basic Research Program of China(973 Program)under Grant No.2005CB321901
文摘In this paper, we put our focus on a variable-coe^cient fifth-order Korteweg-de Vries (fKdV) equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those constraints, some integrable properties are derived, such as the Lax pair and Darboux transformation. Via the Darboux transformation, which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out.
基金Supported by the Natural Science Foundation of Education Committee of Henan Province(2003110003)
文摘By using the homogeneous balance principle(HBP), we derive a Backtund transformation(BT) to the generalized dispersive long wave equation with variable coefficients.Based on the BT, we give many kinds of the exact solutions of the equation, such as, singlesolitary solutions, multi-soliton solutions and generalized exact solutions.
基金The project supported by the Key Project of the Ministry of Education under Grant No.106033the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20060006024+2 种基金National Natural Science Foundation of China under Grant Nos.60372095 and 60772023the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.SKLSDE07-001Beijing University of Aeronautics and Astronautics,and the National Basic Research Program of China(973 Program)under Grant No.2005CB321901
文摘In this paper, we derive the bilinear form for a variable-coefficient Kadomtsev Petviashvili-typed equation. Based on the bilinear form, we obtain the Wronskian determinant solution, which is proved to be indeed an exact solution of this equation through the Wronskian technique. In addition, we testify that this equation can be reduced to a Jacobi identity by considering its solution as a Grammian determinant by means of Pfaffian derivative formulae.
基金supported by National Natural Science Foundation of China under Grant Nos.60772023 and 60372095the Key Project of the Ministry of Education under Grant No.106033+2 种基金the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.SKLSDE-07-001Beijing University of Aeronautics and Astronautics,the National Basic Research Program of China(973 Program)under Grant No.2005CB321901the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20060006024,the Ministry of Education
文摘By the symbolic computation and Hirota method, the bilinear form and an auto-Backlund transformation for a variable-coemcient Korteweg-de Vries equation with nonuniformities are given. Then, the N-solitonic solution in terms of Wronskian form is obtained and verified. In addition, it is shown that the (N - 1)- and N-solitonic solutions satisfy the auto-Backlund transformation through the Wronskian technique.
基金The project supported by Liu Hui Applied Mathematics Center of Nankai University and 985 Education Development Plan of Tianjin University
文摘We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.
基金The project supported by National Natural Science Foundation of China undcr Grant No. 10172056 .
文摘In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the (2+1)-dimensional variable coefficients Broer-Kaup (VCBK) equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.
文摘In this paper, we extend the mapping transformation method through introducing variable coefficients.By means of the extended mapping transformation method, many explicit and exact general solutions with arbitrary functions for some nonlinear partial differential equations, which contain solitary wave solutions, trigonometric function solutions, and rational solutions, are obtained.
文摘The vector susceptibility is investigated numerically in the Dyson-Schwinger approach. The results agree with those obtained analytically previously by using a simple gluon propagator.
基金funded by the Fundamental Research Funds for the Central Universities (No.201262017)the National Natural Science Foundation of China (No.41210008)
文摘Abstract Selection of net with a suitable mesh size is a key concern in the quantitative assessment of zooplankton, which is cru- cial to understand pelagic ecosystem processes. This study compared the copepod collecting efficiency of three commonly used plankton nets, namely, the China standard coarse net (505 gm mesh), the China standard fine net (77 gin), and the WP-2 net (200 μm) The experiment was performed at six stations in the Bohai Sea during the autumn of 2012. The coarse net substantially un- der-sampled small individuals (body widths 〈 672 gm) and led to the lowest species number in each tow, whereas the fine net col- lected all small copepod species but failed to collect rare species. The WP-2 net appeared to be a compromise of the two other nets, collecting both small copepods and rare species. The abundance of copepods collected by the coarse net (126.4±86.5 indm-3) was one to two orders of magnitude lower than that by the WP-2 net (5802.4 ± 2595.4 indm3), and the value of the fine net (11117.0±4563.41 indm-3) was nearly twice that of the WP-2 net. The abundance of large copepods (i.e., adult Calanus sinicus) in the three nets showed no significant differences, but the abundance of small copepods declined with decreasing mesh size. The dif- ference in abundance resulted from the under-sampling of small copepods with body widths 〈 672 μm and 〈 266μm by the coarse and WP-2 nets, respectively.
基金The project supported by the Natural Science Foundation of Shandong Province under Grant Nos. 2004zx16 and Q2005A01
文摘In this paper, the generalized ranch function method is extended to (2+1)-dimensianal canonical generalized KP (CGKP) equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit exact solutions, which contain multiple soliton-like and periodic solutions, are obtained for the (2+1)-dimensional OGKP equation with variable coetffcients.
基金Project(20080431380) supported by China Postdoctoral Science Foundation
文摘Abstract: A joint solution model of variabk:-mass flow in two-phase region and fluid-solid coupling heat transfer, concerned about the charge process of variable-mass thermodynamic system, is built up and calculated by the finite element method (FEM). The results are basically consistent with relative experimental data. The calculated average heat transfer coefficient reaches 1.7~105 W/(m2. K). When the equal percentage valve is used, the system needs the minimum requirements of valve control, but brings the highest construction cost. With the: decrease of initial steam pressure, the heat transfer intensity also weakens but the steam flow increases. With the initial water filling coefficient increasing or the temperature of steam supply decreasing, the amount of accumulative steam flow increases with the growth of steam pressure. When the pressure of steam supply drops, the steam flow gradient increases during the maximum opening period of control valve, and causes the maximum steam flow to increase.
基金Supported by the National Natural Science Foundation of China under Grant No. 11204242 China Postdoctoral Foundation under Grant No. 2011M501477
文摘Based on existing low-frequency water-filled impedance tube testing facilities, which is a part of the Low Frequency Facility of the Naval Undersea Warfare Center in Beijing, an improved water-filled pulse tube method is presented in this short paper. This proposed study is significantly different from the conventional pulse tube method because of the capability for a single plane damped sine pulse wave to generate in the water-filled pulse tube with a regular waveform and short duration time of about 1ms. During the generation process of the pulse, an inverse filter principle was adopted to compensate the transducer response. The effect of the characteristics of tube termination can be eliminated through the generation process of the pulse. Reflection coefficient from a water/air interface was measured to verify the proposed method. When compared with the expected theoretical values, a relatively good agreement can be obtained in the low frequency range of 500-2 000 Hz.
基金Project(2011ZX05000-026-004) supported by the National Science & Technology Specific Program of ChinaProject(2010D-5006-0604) supported by the China National Petroleum Corporation (CNPC) Innovation FoundationProject(51004167) supported by the National Natural Science Foundation of China
文摘Based on the energy equation of gas-liquid flow in pipeline,the explicit temperature drop formula for gas-liquid steady state calculation was derived.This formula took into consideration the Joule-Thomson effect,impact of terrain undulation and heat transfer with the surroundings along the line.Elimination of temperature iteration loop and integration of the explicit temperature equation,instead of enthalpy energy equation,into the conjugated hydraulic and thermal computation have been found to improve the efficiency of algorithm.Then,the inner wall temperature of gas-liquid flow was calculated by using explicit temperature equation and inner wall convective heat transfer coefficient of mixed flow which can be obtained by liquid convective heat transfer coefficient and gas convective heat transfer coefficient on the basis of liquid holdup.The temperature results of gas-liquid flow and inner wall in the case example presented both agree well with those in professional multiphase computational software OLGA.
基金supported by the National Natural Science Foundation of China under Grant Nos.10125521 and 60371013the 973 National Basic Pesearch and Development Program of China under Contract No.G2000077400
文摘We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for such a system are given, they have the same forms as those for the usual harmonic oscillator with constant mass. The coherent state and its properties corresponding effective potentials for several mass functions, for the system with PDM are also discussed. We give the the systems with such potentials are isospectral to the usual harmonic oscillator.
基金Supported by National Natural Science Foundation of China (No.60820106002,No.60532020)Natural Science Foundation of Tianjin(No.11JCYBJC06900)
文摘In this paper, a novel reconstruction technique based on level set method and algebraic reconstruction technique is proposed for multiphase flow computed tomography (CT) system. The curvature-driven noise reduction method is inserted into the conventional iteration procedure of algebraic reconstruction technique to improve the image quality and convergence speed with limited projection data. By evolving the image as a set of iso-intensity contours after each updation, the sufficient number of iterations for acceptable results is reduced by 80%-90%, while the image quality is enhanced obviously. Quantitative evaluation of image quality is given by using both relative image error and correlation coefficient. The resultant images can be utilized to detect flow regimes for monitoring industrial multiphase flow. Laboratory results demonstrate the feasibility of the proposed method. Phantoms of four typical flow regimes can be reconstructed from few-view projection data efficiently, and the corresponding image errors and correlation coefficients are acceptable for the cases tested in this paper.