Using the solution of general Korteweg-de Vries （KdV） equation, the solutions of the generalized variable coefficient Kadomtsev-Petviashvili （KP） equation are constructed, and then its new solitary wave-like solut...Using the solution of general Korteweg-de Vries （KdV） equation, the solutions of the generalized variable coefficient Kadomtsev-Petviashvili （KP） equation are constructed, and then its new solitary wave-like solution and Jacobi elliptic function solution are obtained.展开更多
The purpose of this paper is to introduce a class of generaJized nonlinear evolution equations, which can be widely applied to describing a variety of phenomena in nonlinear physical science. A KdV-type Wronskian form...The purpose of this paper is to introduce a class of generaJized nonlinear evolution equations, which can be widely applied to describing a variety of phenomena in nonlinear physical science. A KdV-type Wronskian formulation is constructed by employing the Wronskian conditions of the KdV equation. Applications are made for the （3＋1）- dimensional generalized KP, BKP and Jimbo-Miwa equations, thereby presenting their Wronskian sufficient conditions. An N-soliton solution in terms of Wronskian determinant is obtained. Under a dimensional reduction, our results yield Wronskian solutions of the KdV equation.展开更多
In this paper, we use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the modified KdV-KP equations. Some explicit periodic wave solutions are obtained. These solu...In this paper, we use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the modified KdV-KP equations. Some explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain solitary wave solutions, periodic wave solutions, kink wave solutions and unbounded solutions.展开更多
This paper studied new class of integral equation called the Korteweg-de Vries-Kadomtsev-Petviashvili(KdV-KP)equation.This equation consist of the well-known fifth-order KdV equation in the context of the Kadomtsev-Pe...This paper studied new class of integral equation called the Korteweg-de Vries-Kadomtsev-Petviashvili(KdV-KP)equation.This equation consist of the well-known fifth-order KdV equation in the context of the Kadomtsev-Petviashvili equation.The newly gathered class of sixth-order KdV-KP equation is studied using the sub-equation method to obtain several soliton-type solutions which consist of trigonometric,hyperbolic,and rational solutions.The application of the sub-equation approach in this work draws attention to the outstanding characteristics of the suggested method and its ability to handle completely integrable equations.Furthermore,the obtained solutions have not been reported in the previous literature and might have significant impact on future research.展开更多
文摘Using the solution of general Korteweg-de Vries （KdV） equation, the solutions of the generalized variable coefficient Kadomtsev-Petviashvili （KP） equation are constructed, and then its new solitary wave-like solution and Jacobi elliptic function solution are obtained.
基金Supported by the National Natural Science Foundation of China under Grant No.11371326
文摘The purpose of this paper is to introduce a class of generaJized nonlinear evolution equations, which can be widely applied to describing a variety of phenomena in nonlinear physical science. A KdV-type Wronskian formulation is constructed by employing the Wronskian conditions of the KdV equation. Applications are made for the （3＋1）- dimensional generalized KP, BKP and Jimbo-Miwa equations, thereby presenting their Wronskian sufficient conditions. An N-soliton solution in terms of Wronskian determinant is obtained. Under a dimensional reduction, our results yield Wronskian solutions of the KdV equation.
基金Supported by National Natural Science Foundation of China(Grant Nos.11361069 and 11171115)
文摘In this paper, we use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the modified KdV-KP equations. Some explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain solitary wave solutions, periodic wave solutions, kink wave solutions and unbounded solutions.
文摘This paper studied new class of integral equation called the Korteweg-de Vries-Kadomtsev-Petviashvili(KdV-KP)equation.This equation consist of the well-known fifth-order KdV equation in the context of the Kadomtsev-Petviashvili equation.The newly gathered class of sixth-order KdV-KP equation is studied using the sub-equation method to obtain several soliton-type solutions which consist of trigonometric,hyperbolic,and rational solutions.The application of the sub-equation approach in this work draws attention to the outstanding characteristics of the suggested method and its ability to handle completely integrable equations.Furthermore,the obtained solutions have not been reported in the previous literature and might have significant impact on future research.
