This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations . Starting from the homogeneous ba...This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations . Starting from the homogeneous balance method, we find that the richness of the localized coherent structures of the model is caused by the entrance of two variable-separated arbitrary functions. For some special selections of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, breathers, instantons and ring solitons.展开更多
Using the extended homogeneous balance method, we find some special types of single solitary wave solution and new types of the multisoliton solutions of the (3+1)-dimensional Jimbo-Miwa equation.
Using extended homogeneous balance method and variable separation hypothesis, we found new variable separation solutions with three arbitrary functions of the （2＋1）-dimensional dispersive long-wave equations, Based...Using extended homogeneous balance method and variable separation hypothesis, we found new variable separation solutions with three arbitrary functions of the （2＋1）-dimensional dispersive long-wave equations, Based on derived solutions, we revealed abundant oscillating solitons such as dromion, multi-dromion, solitoff, solitary waves, and so on, by selecting appropriate functions.展开更多
By the application of the extended homogeneous balance method, we derive anauto-Backlund transformation (BT) for (2+1)-dimensional variable coefficient generalized KPequations. Based on the BT, in which there are two ...By the application of the extended homogeneous balance method, we derive anauto-Backlund transformation (BT) for (2+1)-dimensional variable coefficient generalized KPequations. Based on the BT, in which there are two homogeneity equations to be solved, we obtainsome exact solutions containing single solitary waves.展开更多
Abstract By improving the extended homogeneous balance method, a general method is suggested to derive a new auto-Bgcklund transformation （BT） for （3-k l）-Dimensional Jimbo-Miwa （JM） equation. The auto-BT obtain...Abstract By improving the extended homogeneous balance method, a general method is suggested to derive a new auto-Bgcklund transformation （BT） for （3-k l）-Dimensional Jimbo-Miwa （JM） equation. The auto-BT obtained by using our method only involves one quadratic homogeneity equation written as a bilinear equation. Based on the auto-BT, two-soliton solution of the （3＋1）-Dimensional JM equation is obtained.展开更多
Using the extended homogeneous balance method, we obtained abundant exact solution structures ofthe (3 + 1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation. By means of the leading order term analysis, thenonlinear...Using the extended homogeneous balance method, we obtained abundant exact solution structures ofthe (3 + 1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation. By means of the leading order term analysis, thenonlinear transformations of the (3+1)-dimensional NNV equation are given first, and then some special types of singlesolitary wave solution and the multisoliton solutions are constructed.展开更多
An extended homogeneous balance method is suggested in this paper.Based on computerized symbolic computation and the homogeneous balance method,new exact traveling wave solutions of nonlinear partial differential equa...An extended homogeneous balance method is suggested in this paper.Based on computerized symbolic computation and the homogeneous balance method,new exact traveling wave solutions of nonlinear partial differential equations(PDEs)are presented.The shallow-water equations represent a simple yet realistic set of equations typically found in atmospheric or ocean modeling applications,we consider the exact solutions of the nonlinear generalized shallow water equation and the fourth order Boussinesq equation.Applying this method,with the aid of Mathematica,many new exact traveling wave solutions are successfully obtained.展开更多
In this paper,several new constant-amplitude and variable-amplitude wave solutions（namely,traveling wave solutions） of a generalized nonlinear Schrdinger equation are investigated by using the extended homogeneous b...In this paper,several new constant-amplitude and variable-amplitude wave solutions（namely,traveling wave solutions） of a generalized nonlinear Schrdinger equation are investigated by using the extended homogeneous balance method,where the balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation,respectively.In addition,stability analysis of those solutions are also conducted by regular phase plane technique.展开更多
文摘This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations . Starting from the homogeneous balance method, we find that the richness of the localized coherent structures of the model is caused by the entrance of two variable-separated arbitrary functions. For some special selections of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, breathers, instantons and ring solitons.
文摘Using the extended homogeneous balance method, we find some special types of single solitary wave solution and new types of the multisoliton solutions of the (3+1)-dimensional Jimbo-Miwa equation.
基金The project supported by the Natural Science Foundation of Inner Mongolia under Grant No. 200408020113 and National Natural Science Foundation of China under Grant No. 40564001
文摘Using extended homogeneous balance method and variable separation hypothesis, we found new variable separation solutions with three arbitrary functions of the （2＋1）-dimensional dispersive long-wave equations, Based on derived solutions, we revealed abundant oscillating solitons such as dromion, multi-dromion, solitoff, solitary waves, and so on, by selecting appropriate functions.
文摘By the application of the extended homogeneous balance method, we derive anauto-Backlund transformation (BT) for (2+1)-dimensional variable coefficient generalized KPequations. Based on the BT, in which there are two homogeneity equations to be solved, we obtainsome exact solutions containing single solitary waves.
基金Supported by National Natural Science Foundation of China under Grant No.11071209 the Natural Science Foundation of the Higer Education Institutions of Jiangsu Province under Grant No.10KJB110011
文摘Abstract By improving the extended homogeneous balance method, a general method is suggested to derive a new auto-Bgcklund transformation （BT） for （3-k l）-Dimensional Jimbo-Miwa （JM） equation. The auto-BT obtained by using our method only involves one quadratic homogeneity equation written as a bilinear equation. Based on the auto-BT, two-soliton solution of the （3＋1）-Dimensional JM equation is obtained.
基金The project supported by National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province
文摘Using the extended homogeneous balance method, we obtained abundant exact solution structures ofthe (3 + 1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation. By means of the leading order term analysis, thenonlinear transformations of the (3+1)-dimensional NNV equation are given first, and then some special types of singlesolitary wave solution and the multisoliton solutions are constructed.
文摘An extended homogeneous balance method is suggested in this paper.Based on computerized symbolic computation and the homogeneous balance method,new exact traveling wave solutions of nonlinear partial differential equations(PDEs)are presented.The shallow-water equations represent a simple yet realistic set of equations typically found in atmospheric or ocean modeling applications,we consider the exact solutions of the nonlinear generalized shallow water equation and the fourth order Boussinesq equation.Applying this method,with the aid of Mathematica,many new exact traveling wave solutions are successfully obtained.
基金supported by the National NSF of China(11571088)NSF of Zhejiang Province(LY13A010020)Program(HNUEYT2013)
文摘In this paper,several new constant-amplitude and variable-amplitude wave solutions（namely,traveling wave solutions） of a generalized nonlinear Schrdinger equation are investigated by using the extended homogeneous balance method,where the balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation,respectively.In addition,stability analysis of those solutions are also conducted by regular phase plane technique.
