Links between some (2 + 1)-dimensional nonlinear evolution equations and Painlevé-II equations

Mei Jianqin; Huang Dingjiang; Zhang Hongqing

doi:10.1016/j.cnsns.2009.02.026

Links between some (2 + 1)-dimensional nonlinear evolution equations and Painlevé-II equations

Mei Jianqin^*
, Huang Dingjiang
, Zhang Hongqing

^*Corresponding author for this work

Dalian University of Technology
East China University of Science and Technology

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

Abstract

Using the idea of transformation, some links between (2 + 1)-dimensional nonlinear evolution equations and the ordinary differential equations Painlevé-II equations has been illustrated. The Kadomtsev-Petviashvili (KP) equation, generalized (2 + 1)-dimensional break soliton equation and (2 + 1)-dimensional Boussinesq equation are researched. As a result, some new interesting results about these (2 + 1)-dimensional PDEs have been obtained, such as the exact solutions with arbitrary functions, rich rational solutions and the nontrivial Bäcklund transformations have been derived.

Original language	English
Pages (from-to)	3798-3803
Number of pages	6
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	14
Issue number	11
DOIs	https://doi.org/10.1016/j.cnsns.2009.02.026
State	Published - Nov 2009
Externally published	Yes

Keywords

(2 + 1)-Dimensional nonlinear evolution equations
Bäcklund transformation
Rational solution
The second Painlevé equation

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10.1016/j.cnsns.2009.02.026

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title = "Links between some (2 + 1)-dimensional nonlinear evolution equations and Painlev{\'e}-II equations",

abstract = "Using the idea of transformation, some links between (2 + 1)-dimensional nonlinear evolution equations and the ordinary differential equations Painlev{\'e}-II equations has been illustrated. The Kadomtsev-Petviashvili (KP) equation, generalized (2 + 1)-dimensional break soliton equation and (2 + 1)-dimensional Boussinesq equation are researched. As a result, some new interesting results about these (2 + 1)-dimensional PDEs have been obtained, such as the exact solutions with arbitrary functions, rich rational solutions and the nontrivial B{\"a}cklund transformations have been derived.",

keywords = "(2 + 1)-Dimensional nonlinear evolution equations, B{\"a}cklund transformation, Rational solution, The second Painlev{\'e} equation",

author = "Mei Jianqin and Huang Dingjiang and Zhang Hongqing",

year = "2009",

month = nov,

doi = "10.1016/j.cnsns.2009.02.026",

language = "英语",

volume = "14",

pages = "3798--3803",

journal = "Communications in Nonlinear Science and Numerical Simulation",

issn = "1007-5704",

publisher = "Elsevier B.V.",

number = "11",

}

TY - JOUR

T1 - Links between some (2 + 1)-dimensional nonlinear evolution equations and Painlevé-II equations

AU - Jianqin, Mei

AU - Dingjiang, Huang

AU - Hongqing, Zhang

PY - 2009/11

Y1 - 2009/11

N2 - Using the idea of transformation, some links between (2 + 1)-dimensional nonlinear evolution equations and the ordinary differential equations Painlevé-II equations has been illustrated. The Kadomtsev-Petviashvili (KP) equation, generalized (2 + 1)-dimensional break soliton equation and (2 + 1)-dimensional Boussinesq equation are researched. As a result, some new interesting results about these (2 + 1)-dimensional PDEs have been obtained, such as the exact solutions with arbitrary functions, rich rational solutions and the nontrivial Bäcklund transformations have been derived.

AB - Using the idea of transformation, some links between (2 + 1)-dimensional nonlinear evolution equations and the ordinary differential equations Painlevé-II equations has been illustrated. The Kadomtsev-Petviashvili (KP) equation, generalized (2 + 1)-dimensional break soliton equation and (2 + 1)-dimensional Boussinesq equation are researched. As a result, some new interesting results about these (2 + 1)-dimensional PDEs have been obtained, such as the exact solutions with arbitrary functions, rich rational solutions and the nontrivial Bäcklund transformations have been derived.

KW - (2 + 1)-Dimensional nonlinear evolution equations

KW - Bäcklund transformation

KW - Rational solution

KW - The second Painlevé equation

UR - https://www.scopus.com/pages/publications/67349205022

U2 - 10.1016/j.cnsns.2009.02.026

DO - 10.1016/j.cnsns.2009.02.026

M3 - 文章

AN - SCOPUS:67349205022

SN - 1007-5704

VL - 14

SP - 3798

EP - 3803

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 11

ER -

Links between some (2 + 1)-dimensional nonlinear evolution equations and Painlevé-II equations

Abstract

Keywords

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