In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations....In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.展开更多
Interracial internal waves in a three-layer density-stratified fluid are investigated using a singular perturbation method, and third-order asymptotic solutions of the velocity potentials and third-order Stokes wave s...Interracial internal waves in a three-layer density-stratified fluid are investigated using a singular perturbation method, and third-order asymptotic solutions of the velocity potentials and third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. As expected, the third-order solutions describe the third-order nonlinear modification and the third-order nonlinear interactions between the interracial waves. The wave velocity depends on not only the wave number and the depth of each layer but also on the wave amplitude.展开更多
Painleve integrability has been tested for （2＋1）D Boussinesq equation with disturbance term using the standard WTC approach after introducing the Kruskai＇s simplification. New breather solitary solutions depending...Painleve integrability has been tested for （2＋1）D Boussinesq equation with disturbance term using the standard WTC approach after introducing the Kruskai＇s simplification. New breather solitary solutions depending on constant equilibrium solution are obtained by using Extended Homoclinic Test Method. Moreover, the spatiotemporal feature of breather solitary wave is exhibited.展开更多
The compound KdV-type equation with nonlinear terms of any order is reduced to the integral form. Using the complete discrimination system for polynomial, its all possible exact traveling wave solutions are obtained. ...The compound KdV-type equation with nonlinear terms of any order is reduced to the integral form. Using the complete discrimination system for polynomial, its all possible exact traveling wave solutions are obtained. Among those, a lot of solutions are new.展开更多
Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solut...Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.展开更多
Burgers equation is the simplest one in soliton theory, which has been widely applied in almost all the physical branches. In this paper, we discuss the Painleve property of the （3＋1）-dimensional Burgers equation, ...Burgers equation is the simplest one in soliton theory, which has been widely applied in almost all the physical branches. In this paper, we discuss the Painleve property of the （3＋1）-dimensional Burgers equation, and then Becklund transformation is derived according to the truncated expansion of the obtained Painleve analysis. Using the Backlund transformation, we find the rouge wave solutions to the equation via the multilinear variable separation approach. And we aiso give an exact solution obtained by general variable separation approach, which is proved to possess abundant structures.展开更多
Based on the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method, the first elliptic function equation is used to get a new kind of solutions of nonlinear evolution equat...Based on the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method, the first elliptic function equation is used to get a new kind of solutions of nonlinear evolution equations. New exact solutions to the Jacobi elliptic function of MKdV equations and Benjamin-Bona-Mahoney （BBM） equations are obtained with the aid of computer algebraic system Maple. The method is also valid for other （l＋l）-dimensional and higher dimensional systems.展开更多
文摘In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.
基金supported by the Natural Science Foundation of Inner Mongolia,China(Grant No 200711020116)Open Fund of the Key Laboratory of Ocean Circulation and Waves,Chinese Academy of Sciences(Grant No KLOCAW0805)+1 种基金the Key Program of the Scientific Research Plan of Inner Mongolia University of Technology,China(Grant No ZD200608)National Science Fund for Distinguished Young Scholars of China(Grant No 40425015)
文摘Interracial internal waves in a three-layer density-stratified fluid are investigated using a singular perturbation method, and third-order asymptotic solutions of the velocity potentials and third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. As expected, the third-order solutions describe the third-order nonlinear modification and the third-order nonlinear interactions between the interracial waves. The wave velocity depends on not only the wave number and the depth of each layer but also on the wave amplitude.
基金Supported by National Natural Science Foundation of China under Grant Nos. 11061028, 11261049, Yunnan Natural Science Foundation under Grant Nos. 2010CD086 and 2011Y012 and Qujing Normal University Natural Science Foundation under Grant Nos. 2009ZD002 and 2012QN016
文摘Painleve integrability has been tested for （2＋1）D Boussinesq equation with disturbance term using the standard WTC approach after introducing the Kruskai＇s simplification. New breather solitary solutions depending on constant equilibrium solution are obtained by using Extended Homoclinic Test Method. Moreover, the spatiotemporal feature of breather solitary wave is exhibited.
基金The project supported by Scientific Reseaxch Fund of Education Department of Heilongjiang Province of China under Grant No. 11511008
文摘The compound KdV-type equation with nonlinear terms of any order is reduced to the integral form. Using the complete discrimination system for polynomial, its all possible exact traveling wave solutions are obtained. Among those, a lot of solutions are new.
文摘Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.
基金Supported by National Natural Science Foundation of China under Grant Nos.11175092,11275123,11205092Ningbo University Discipline Project under Grant No.xkzl1008K.C.Wong Magna Fund in Ningbo University
文摘Burgers equation is the simplest one in soliton theory, which has been widely applied in almost all the physical branches. In this paper, we discuss the Painleve property of the （3＋1）-dimensional Burgers equation, and then Becklund transformation is derived according to the truncated expansion of the obtained Painleve analysis. Using the Backlund transformation, we find the rouge wave solutions to the equation via the multilinear variable separation approach. And we aiso give an exact solution obtained by general variable separation approach, which is proved to possess abundant structures.
基金Supported by the National Natural Science Foundation of China (No. 10647112)the Foundation of Donghua University
文摘Based on the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method, the first elliptic function equation is used to get a new kind of solutions of nonlinear evolution equations. New exact solutions to the Jacobi elliptic function of MKdV equations and Benjamin-Bona-Mahoney （BBM） equations are obtained with the aid of computer algebraic system Maple. The method is also valid for other （l＋l）-dimensional and higher dimensional systems.
