This paper uses the boundary layer theory to obtain an asymptotic solution of the nonlinear educed wave equation. This solution is valid in the secular region where the geometrical optics result fails. However it agre...This paper uses the boundary layer theory to obtain an asymptotic solution of the nonlinear educed wave equation. This solution is valid in the secular region where the geometrical optics result fails. However it agrees with the geometrical optics result when the field is away from the secular region. By using this solution the self-focusing length can also be obtained.展开更多
In this paper, we study soliton-cnoidal wave solutions for the reduced Maxwell-Bloch equations. The truncated Painlev6 analysis is utilized to generate a consistent Riccati expansion, which leads to solving the reduce...In this paper, we study soliton-cnoidal wave solutions for the reduced Maxwell-Bloch equations. The truncated Painlev6 analysis is utilized to generate a consistent Riccati expansion, which leads to solving the reduced Maxwell-Bloch equations with solitary wave, cnoidal periodic wave, and soliton-cnoidal interactional wave solutions in an explicit form. Particularly, the soliton-cnoidal interactional wave solution is obtained for the first time for the reduced Maxwell-Bloch equations. Finally, we present some figures to show properties of the explicit soliton-cnoidal interactional wave solutions as well as some new dynamical phenomena.展开更多
The PnP problem is a widely used technique for pose determination in computer vision community,and finding out geometric conditions of multiple solutions is the ultimate and most desirable goal of the multi-solution a...The PnP problem is a widely used technique for pose determination in computer vision community,and finding out geometric conditions of multiple solutions is the ultimate and most desirable goal of the multi-solution analysis,which is also a key research issue of the problem.In this paper,we prove that given 3 control points,if the camera's optical center lies on the so-called“danger cylinder”and is enough far from the supporting plane of control points,the corresponding P3P problem must have 3 positive solutions.This result can bring some new insights into a better understanding of the multi-solution problem.For example,it is shown in the literature that the solution of the P3P problem is instable if the optical center lies on this danger cylinder,we think such occurrence of triple-solution is the primary source of this instability.展开更多
We study a simplified(3+1)-dimensional model equation and construct a lump solution for the special case of z=y using the Hirota bilinear method.Then,a more general form of lump solution is constructed,which contains ...We study a simplified(3+1)-dimensional model equation and construct a lump solution for the special case of z=y using the Hirota bilinear method.Then,a more general form of lump solution is constructed,which contains more arbitrary autocephalous parameters.In addition,a lumpoff solution is also derived based on the general lump solutions and a stripe soliton.Furthermore,we figure out instanton/rogue wave solutions via introducing two stripe solitons.Finally,one can better illustrate these propagation phenomena of these solutions by analyzing images.展开更多
In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution ...In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution to the special case for z=x.Furthermore,a more general form of lump solution of the equation is found which possesses seven arbitrary parameters and four constraint conditions.By cutting the lump by the induced soliton(s),lumpoff and instanton/rogue wave solutions are also constructed by the more general form of lump solution.展开更多
In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.T...In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.展开更多
In this paper, we investigate symmetries of the new (4+1)-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symm...In this paper, we investigate symmetries of the new (4+1)-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symmetries. And then we transform the Fokas equation into a potential system and gain the potential symmetries of Fokas equation. Finally, we use the obtained point symmetries wave solutions and other solutions of the Fokas equation. and some constructive methods to get some doubly periodic In particular, some solitary wave solutions are also given.展开更多
In this paper, we use the classical Lie group symmetry method to get the Lie point symmetries of the (2+1)-dimensional hyperbolic nonlinear Schr6dinger (HNLS) equation and reduce the (2+1)-dimensional HNLS equ...In this paper, we use the classical Lie group symmetry method to get the Lie point symmetries of the (2+1)-dimensional hyperbolic nonlinear Schr6dinger (HNLS) equation and reduce the (2+1)-dimensional HNLS equation to some (1 + 1 )-dimensional partial differential systems. Finally, many exact travelling solutions of the (2+1)-dimensional HNLS equation are obtained by the classical Lie symmetry reduced method.展开更多
ZTE’s cost-effective GSM solutions provide world class service to over 70 million subscribers in more than 30 countries,and have helped us build strong partnerships with 12 of the world’s top thirty telecoms operators.
The drag-reducing characteristics of a cationic surfactant solution flow in copper pipe have been investigated experimentally.The tested drag-reducing fluid was an aqueous solution of the cationic surfactant cetyltrim...The drag-reducing characteristics of a cationic surfactant solution flow in copper pipe have been investigated experimentally.The tested drag-reducing fluid was an aqueous solution of the cationic surfactant cetyltrimethyl ammonium chloride(CTAC).The experimental results show that the maximum drag reduction percentage reduces with the increase of fluid temperature at low concentration of CTAC,such as 100×10-6 or 150×10-6.Furthermore,the concentration and temperature changes of CTAC solution have significant influences on the drag-reducing ability.The drag-reducing effect of CTAC additives shows great potentials in the application in a district heating/cooling(DHC)system,especially for the radiant floor heating(RFH)system.展开更多
Cu2O@Cu2O core-shell nanoparticles (NPs) were prepared by using solution phase strategy. It was found that Cu2O@Cu2O NPs were easily converted to Cu2O@Cu NPs with the help of polyvinylpyrrolidine (PVP) and excessive a...Cu2O@Cu2O core-shell nanoparticles (NPs) were prepared by using solution phase strategy. It was found that Cu2O@Cu2O NPs were easily converted to Cu2O@Cu NPs with the help of polyvinylpyrrolidine (PVP) and excessive ascorbic acid (AA) in air at room temperature, which was an interesting phenomenon. The features of the two kinds of NPs were characterized by XRD, TEM and extinction spectra. Cu2O@Cu NPs with different shell thicknesses showed wide tunable optical properties for the localized surface plasmon (LSP) in metallic Cu. But Cu2O@Cu2O NPs did not indicate this feature. FTIR results reveal that Cu+ ions on the surface of Cu2O shell coordinate with N and O atoms in PVP and are further reduced to metallic Cu by excessive AA and then form a nucleation site on the surface of Cu2O nanocrystalline. PVP binds onto different sites to proceed with the reduction utill all the Cu sources in Cu2O shell are completely assumed.展开更多
In this paper,we prove an infinite dimensional KAM theorem and apply it to study 2-dimensional nonlinear Schrodinger equations with different large forcing terms and(2p+1)-nonlinearities iu_(t)-Δu+φ_(1)(ω_(1)+t)u+...In this paper,we prove an infinite dimensional KAM theorem and apply it to study 2-dimensional nonlinear Schrodinger equations with different large forcing terms and(2p+1)-nonlinearities iu_(t)-Δu+φ_(1)(ω_(1)+t)u+φ_(2)(ω_(2)+t)|u|^(2p)u=0,t∈R,x∈T^(2) under periodic boundary conditions. As a result, the existence of a Whitneysmooth family of small-amplitude reducible quasi-periodic solutions is obtained.展开更多
文摘This paper uses the boundary layer theory to obtain an asymptotic solution of the nonlinear educed wave equation. This solution is valid in the secular region where the geometrical optics result fails. However it agrees with the geometrical optics result when the field is away from the secular region. By using this solution the self-focusing length can also be obtained.
基金Project supported by the Global Change Research Program of China(Grant No.2015CB953904)the National Natural Science Foundation of China(Grant Nos.11675054 and 11435005)+3 种基金the Outstanding Doctoral Dissertation Cultivation Plan of Action(Grant No.YB2016039)Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things(Grant No.ZF1213)the UTRGV President Endowed Professorship(Grant No.450000123)the UTRGV College of Science Seed Grant(Grant No.240000013)for partial support
文摘In this paper, we study soliton-cnoidal wave solutions for the reduced Maxwell-Bloch equations. The truncated Painlev6 analysis is utilized to generate a consistent Riccati expansion, which leads to solving the reduced Maxwell-Bloch equations with solitary wave, cnoidal periodic wave, and soliton-cnoidal interactional wave solutions in an explicit form. Particularly, the soliton-cnoidal interactional wave solution is obtained for the first time for the reduced Maxwell-Bloch equations. Finally, we present some figures to show properties of the explicit soliton-cnoidal interactional wave solutions as well as some new dynamical phenomena.
基金Supported by"973"Program(2002CB312104)National Natural Science Foundation of P.R.China(60375006)the Research Foundation of North China Unversity of Technology University
文摘The PnP problem is a widely used technique for pose determination in computer vision community,and finding out geometric conditions of multiple solutions is the ultimate and most desirable goal of the multi-solution analysis,which is also a key research issue of the problem.In this paper,we prove that given 3 control points,if the camera's optical center lies on the so-called“danger cylinder”and is enough far from the supporting plane of control points,the corresponding P3P problem must have 3 positive solutions.This result can bring some new insights into a better understanding of the multi-solution problem.For example,it is shown in the literature that the solution of the P3P problem is instable if the optical center lies on this danger cylinder,we think such occurrence of triple-solution is the primary source of this instability.
基金Project supported by the National Natural Science Foundation of China(Grant No.11971475)。
文摘We study a simplified(3+1)-dimensional model equation and construct a lump solution for the special case of z=y using the Hirota bilinear method.Then,a more general form of lump solution is constructed,which contains more arbitrary autocephalous parameters.In addition,a lumpoff solution is also derived based on the general lump solutions and a stripe soliton.Furthermore,we figure out instanton/rogue wave solutions via introducing two stripe solitons.Finally,one can better illustrate these propagation phenomena of these solutions by analyzing images.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11675084 and 11435005)the Fund from the Educational Commission of Zhejiang Province,China(Grant No.Y201737177)+1 种基金Ningbo Natural Science Foundation(Grant No.2015A610159)the K C Wong Magna Fund in Ningbo University
文摘In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution to the special case for z=x.Furthermore,a more general form of lump solution of the equation is found which possesses seven arbitrary parameters and four constraint conditions.By cutting the lump by the induced soliton(s),lumpoff and instanton/rogue wave solutions are also constructed by the more general form of lump solution.
文摘In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.
基金supported by the National Natural Science Foundation of China under Grant No.60821002the National Key Basic Research Program of China under Grant No.2004CB318000
文摘In this paper, we investigate symmetries of the new (4+1)-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symmetries. And then we transform the Fokas equation into a potential system and gain the potential symmetries of Fokas equation. Finally, we use the obtained point symmetries wave solutions and other solutions of the Fokas equation. and some constructive methods to get some doubly periodic In particular, some solitary wave solutions are also given.
基金Supported by the National Natural Science Foundation of China under Grant No.10875106
文摘In this paper, we use the classical Lie group symmetry method to get the Lie point symmetries of the (2+1)-dimensional hyperbolic nonlinear Schr6dinger (HNLS) equation and reduce the (2+1)-dimensional HNLS equation to some (1 + 1 )-dimensional partial differential systems. Finally, many exact travelling solutions of the (2+1)-dimensional HNLS equation are obtained by the classical Lie symmetry reduced method.
文摘ZTE’s cost-effective GSM solutions provide world class service to over 70 million subscribers in more than 30 countries,and have helped us build strong partnerships with 12 of the world’s top thirty telecoms operators.
基金Sponsored by the National Nature Science Foundation of China(Grant No.50908064)the Ph.D. Programs Foundation of Ministry of Education of China(Grant No.20090460912)
文摘The drag-reducing characteristics of a cationic surfactant solution flow in copper pipe have been investigated experimentally.The tested drag-reducing fluid was an aqueous solution of the cationic surfactant cetyltrimethyl ammonium chloride(CTAC).The experimental results show that the maximum drag reduction percentage reduces with the increase of fluid temperature at low concentration of CTAC,such as 100×10-6 or 150×10-6.Furthermore,the concentration and temperature changes of CTAC solution have significant influences on the drag-reducing ability.The drag-reducing effect of CTAC additives shows great potentials in the application in a district heating/cooling(DHC)system,especially for the radiant floor heating(RFH)system.
基金Projects(41172110,61107090)supported by the National Natural Science Foundation of China
文摘Cu2O@Cu2O core-shell nanoparticles (NPs) were prepared by using solution phase strategy. It was found that Cu2O@Cu2O NPs were easily converted to Cu2O@Cu NPs with the help of polyvinylpyrrolidine (PVP) and excessive ascorbic acid (AA) in air at room temperature, which was an interesting phenomenon. The features of the two kinds of NPs were characterized by XRD, TEM and extinction spectra. Cu2O@Cu NPs with different shell thicknesses showed wide tunable optical properties for the localized surface plasmon (LSP) in metallic Cu. But Cu2O@Cu2O NPs did not indicate this feature. FTIR results reveal that Cu+ ions on the surface of Cu2O shell coordinate with N and O atoms in PVP and are further reduced to metallic Cu by excessive AA and then form a nucleation site on the surface of Cu2O nanocrystalline. PVP binds onto different sites to proceed with the reduction utill all the Cu sources in Cu2O shell are completely assumed.
文摘In this paper,we prove an infinite dimensional KAM theorem and apply it to study 2-dimensional nonlinear Schrodinger equations with different large forcing terms and(2p+1)-nonlinearities iu_(t)-Δu+φ_(1)(ω_(1)+t)u+φ_(2)(ω_(2)+t)|u|^(2p)u=0,t∈R,x∈T^(2) under periodic boundary conditions. As a result, the existence of a Whitneysmooth family of small-amplitude reducible quasi-periodic solutions is obtained.