Lax pair, auto-Bäcklund transformation and conservation law for a generalized variable-coefficient KdV equation with external-force term

Yuping Zhang; Jing Liu; Guangmei Wei

doi:10.1016/j.aml.2015.01.007

Lax pair, auto-Bäcklund transformation and conservation law for a generalized variable-coefficient KdV equation with external-force term

Yuping Zhang^*
, Jing Liu
, Guangmei Wei

^*此作品的通讯作者

Beihang University

科研成果: 期刊稿件 › 文章 › 同行评审

20 引用（Scopus）

摘要

A generalized variable-coefficient KdV equation with perturbed and external-force terms is investigated in this Letter. Lax pair, Riccati-type auto-Bäcklund transformation and Wahlquist-Estabrook-type auto-Bäcklund transformation (WE-BT) are constructed. Based on the WE-BT, the nonlinear superposition formula is obtained and an infinite number of conservation laws are derived recursively, then the analytic solutions are provided including periodic, one-soliton-like and two-soliton-like solutions with inhomogeneous coefficients, external-force term and eigenvalue.

源语言	英语
页（从-至）	58-63
页数	6
期刊	Applied Mathematics Letters
卷	45
DOI	https://doi.org/10.1016/j.aml.2015.01.007
出版状态	已出版 - 7月 2015

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@article{19e64f0ec42e4679bf8c7986b7860819,

title = "Lax pair, auto-B{\"a}cklund transformation and conservation law for a generalized variable-coefficient KdV equation with external-force term",

abstract = "A generalized variable-coefficient KdV equation with perturbed and external-force terms is investigated in this Letter. Lax pair, Riccati-type auto-B{\"a}cklund transformation and Wahlquist-Estabrook-type auto-B{\"a}cklund transformation (WE-BT) are constructed. Based on the WE-BT, the nonlinear superposition formula is obtained and an infinite number of conservation laws are derived recursively, then the analytic solutions are provided including periodic, one-soliton-like and two-soliton-like solutions with inhomogeneous coefficients, external-force term and eigenvalue.",

keywords = "Auto-B{\"a}cklund transformation, Conservation law, Generalized variable-coefficient, KdV equation, Lax pair, Symbolic computation",

author = "Yuping Zhang and Jing Liu and Guangmei Wei",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Ltd.",

year = "2015",

month = jul,

doi = "10.1016/j.aml.2015.01.007",

language = "英语",

volume = "45",

pages = "58--63",

journal = "Applied Mathematics Letters",

issn = "0893-9659",

publisher = "Elsevier Ltd",

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TY - JOUR

T1 - Lax pair, auto-Bäcklund transformation and conservation law for a generalized variable-coefficient KdV equation with external-force term

AU - Zhang, Yuping

AU - Liu, Jing

AU - Wei, Guangmei

PY - 2015/7

Y1 - 2015/7

N2 - A generalized variable-coefficient KdV equation with perturbed and external-force terms is investigated in this Letter. Lax pair, Riccati-type auto-Bäcklund transformation and Wahlquist-Estabrook-type auto-Bäcklund transformation (WE-BT) are constructed. Based on the WE-BT, the nonlinear superposition formula is obtained and an infinite number of conservation laws are derived recursively, then the analytic solutions are provided including periodic, one-soliton-like and two-soliton-like solutions with inhomogeneous coefficients, external-force term and eigenvalue.

AB - A generalized variable-coefficient KdV equation with perturbed and external-force terms is investigated in this Letter. Lax pair, Riccati-type auto-Bäcklund transformation and Wahlquist-Estabrook-type auto-Bäcklund transformation (WE-BT) are constructed. Based on the WE-BT, the nonlinear superposition formula is obtained and an infinite number of conservation laws are derived recursively, then the analytic solutions are provided including periodic, one-soliton-like and two-soliton-like solutions with inhomogeneous coefficients, external-force term and eigenvalue.

KW - Auto-Bäcklund transformation

KW - Conservation law

KW - Generalized variable-coefficient

KW - KdV equation

KW - Lax pair

KW - Symbolic computation

UR - https://www.scopus.com/pages/publications/85027941523

U2 - 10.1016/j.aml.2015.01.007

DO - 10.1016/j.aml.2015.01.007

M3 - 文章

AN - SCOPUS:85027941523

SN - 0893-9659

VL - 45

SP - 58

EP - 63

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

Lax pair, auto-Bäcklund transformation and conservation law for a generalized variable-coefficient KdV equation with external-force term

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