Exact solutions and multi-symplectic structure of the generalized KdV-type equation

Xiao Feng Yang; Zi Chen Deng; Qing Jun Li; Yi Wei

doi:10.1186/s13662-015-0611-7

Exact solutions and multi-symplectic structure of the generalized KdV-type equation

Xiao Feng Yang
, Zi Chen Deng
, Qing Jun Li
, Yi Wei

School of Aeronautics

Northwestern Polytechnical University Xian

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The homogeneous balance of undetermined coefficients method is proposed to obtain not only exact solutions but also multi-symplectic structure of some nonlinear partial differential equations. Bilinear equation, N-soliton solutions, traveling wave solutions and multi-symplectic structure are obtained by applying the proposed method to the KdV equation. Accordingly, the definition and multi-symplectic structure of the generalized KdV-type equation are given. The proposed method is also a standard and computable method, which can be generalized to deal with some types of nonlinear partial differential equations.

Original language	English
Article number	271
Journal	Advances in Difference Equations
Volume	2015
Issue number	1
DOIs	https://doi.org/10.1186/s13662-015-0611-7
State	Published - 8 Dec 2015

Keywords

bilinear equation
generalized KdV-type equation
homogeneous balance of undetermined coefficients method
multi-symplectic structure
N-soliton solution
traveling wave solution

Access to Document

10.1186/s13662-015-0611-7

Cite this

@article{a8c29d3916324afd9d22539732b6d274,

title = "Exact solutions and multi-symplectic structure of the generalized KdV-type equation",

abstract = "The homogeneous balance of undetermined coefficients method is proposed to obtain not only exact solutions but also multi-symplectic structure of some nonlinear partial differential equations. Bilinear equation, N-soliton solutions, traveling wave solutions and multi-symplectic structure are obtained by applying the proposed method to the KdV equation. Accordingly, the definition and multi-symplectic structure of the generalized KdV-type equation are given. The proposed method is also a standard and computable method, which can be generalized to deal with some types of nonlinear partial differential equations.",

keywords = "bilinear equation, generalized KdV-type equation, homogeneous balance of undetermined coefficients method, multi-symplectic structure, N-soliton solution, traveling wave solution",

author = "Yang, \{Xiao Feng\} and Deng, \{Zi Chen\} and Li, \{Qing Jun\} and Yi Wei",

note = "Publisher Copyright: {\textcopyright} 2015, Yang et al.",

year = "2015",

month = dec,

day = "8",

doi = "10.1186/s13662-015-0611-7",

language = "英语",

volume = "2015",

journal = "Advances in Difference Equations",

issn = "1687-1839",

publisher = "Springer Publishing Company",

number = "1",

}

TY - JOUR

T1 - Exact solutions and multi-symplectic structure of the generalized KdV-type equation

AU - Yang, Xiao Feng

AU - Deng, Zi Chen

AU - Li, Qing Jun

AU - Wei, Yi

PY - 2015/12/8

Y1 - 2015/12/8

N2 - The homogeneous balance of undetermined coefficients method is proposed to obtain not only exact solutions but also multi-symplectic structure of some nonlinear partial differential equations. Bilinear equation, N-soliton solutions, traveling wave solutions and multi-symplectic structure are obtained by applying the proposed method to the KdV equation. Accordingly, the definition and multi-symplectic structure of the generalized KdV-type equation are given. The proposed method is also a standard and computable method, which can be generalized to deal with some types of nonlinear partial differential equations.

AB - The homogeneous balance of undetermined coefficients method is proposed to obtain not only exact solutions but also multi-symplectic structure of some nonlinear partial differential equations. Bilinear equation, N-soliton solutions, traveling wave solutions and multi-symplectic structure are obtained by applying the proposed method to the KdV equation. Accordingly, the definition and multi-symplectic structure of the generalized KdV-type equation are given. The proposed method is also a standard and computable method, which can be generalized to deal with some types of nonlinear partial differential equations.

KW - bilinear equation

KW - generalized KdV-type equation

KW - homogeneous balance of undetermined coefficients method

KW - multi-symplectic structure

KW - N-soliton solution

KW - traveling wave solution

UR - https://www.scopus.com/pages/publications/84941146105

U2 - 10.1186/s13662-015-0611-7

DO - 10.1186/s13662-015-0611-7

M3 - 文章

AN - SCOPUS:84941146105

SN - 1687-1839

VL - 2015

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

M1 - 271

ER -

Exact solutions and multi-symplectic structure of the generalized KdV-type equation

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this