Two types of generalized integrable decompositions and new solitary-wave solutions for the modified Kadomtsev- Petviashvili equation with symbolic computation
نویسندگان
چکیده
The modified Kadomtsev-Petviashvili (mKP) equation is shown in this paper to be decomposable into the first two soliton equations of the 2N -coupled Chen-Lee-Liu and Kaup-Newell hierarchies by respectively nonlinearizing two sets of symmetry Lax pairs. In these two cases, the decomposed (1+1)-dimensional nonlinear systems both have a couple of different Lax representations, which means that there are two linear systems associated with the mKP equation under the same constraint between the potential and eigenfunctions. For each Lax representation of the decomposed (1+1)-dimensional nonlinear systems, the corresponding Darboux transformation is further constructed such that a series of explicit solutions of the mKP equation can be recursively generated with the assistance of symbolic computation. In illustration, four new families of solitary-wave solutions are presented and the relevant stability is analyzed.
منابع مشابه
Exact solutions of distinct physical structures to the fractional potential Kadomtsev-Petviashvili equation
In this paper, Exp-function and (G′/G)expansion methods are presented to derive traveling wave solutions for a class of nonlinear space-time fractional differential equations. As a results, some new exact traveling wave solutions are obtained.
متن کاملBlow up and instability of solitary wave solutions to a generalized Kadomtsev– Petviashvili equation and two-dimensional Benjamin–Ono equations
Blow up and instability of solitary wave solutions to a generalized Kadomtsev– Petviashvili equation and two-dimensional Benjamin–Ono equations BY JIANQING CHEN*, BOLING GUO AND YONGQIAN HAN School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, People’s Republic of China Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, Peopl...
متن کاملTransverse Instability of Periodic Traveling Waves in the Generalized Kadomtsev-Petviashvili Equation
In this paper, we investigate the spectral instability of periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long wavelength transverse perturbations in the generalized Kadomtsev-Petviashvili equation. By analyzing high and low frequency limits of the appropriate periodic Evans function, we derive an orientation index which yields sufficient conditions for such a...
متن کاملA new fractional sub-equation method for solving the space-time fractional differential equations in mathematical physics
In this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative. With the aid of symbolic computation, we choose the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity a...
متن کاملOn the Solutions and Conservation Laws of a Coupled Kadomtsev-Petviashvili Equation
governs the dynamics of solitary waves. Firstly, it was derived to describe shallowwater waves of long wavelength and small amplitude. It is a crucial equation in the theory of integrable systems because it has infinite number of conservation laws, gives multiple-soliton solutions, and has many other physical properties. See, for example, [2] and references therein. An essential extension of th...
متن کامل