A generalized method and general form solutions to the Whitham-Broer-Kaup equation

Yong Chen; Qi Wang; Biao Li

doi:10.1016/j.chaos.2004.02.024

A generalized method and general form solutions to the Whitham-Broer-Kaup equation

Yong Chen^*
, Qi Wang
, Biao Li

^*Corresponding author for this work

Shanghai Jiao Tong University
Dalian University of Technology
Chinese Academy of Sciences

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

36 Scopus citations

Abstract

Based on a more general transformation presented in this paper, a generalized method for finding more types travelling wave solutions of nonlinear evolution equations (NLEEs) is presented and implemented in a computer algebraic system. As an application of the method, Whitham-Broer-Kaup (WBK) equation is studied to illustrate the method. As a result, We cannot only successfully recover the previously known travelling wave solutions found by Fan's method [J. Phys. A 35 (2002) 6853; Comput. Phys. Commun. 53 (2003) 17], but also obtain some new formal solutions. The solutions obtained in this paper include polynomial, exponential, solitary wave, rational, triangular periodic, Jacobi and Weierstrass doubly periodic solutions.

Original language	English
Pages (from-to)	675-682
Number of pages	8
Journal	Chaos, Solitons and Fractals
Volume	22
Issue number	3
DOIs	https://doi.org/10.1016/j.chaos.2004.02.024
State	Published - Nov 2004
Externally published	Yes

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title = "A generalized method and general form solutions to the Whitham-Broer-Kaup equation",

abstract = "Based on a more general transformation presented in this paper, a generalized method for finding more types travelling wave solutions of nonlinear evolution equations (NLEEs) is presented and implemented in a computer algebraic system. As an application of the method, Whitham-Broer-Kaup (WBK) equation is studied to illustrate the method. As a result, We cannot only successfully recover the previously known travelling wave solutions found by Fan's method [J. Phys. A 35 (2002) 6853; Comput. Phys. Commun. 53 (2003) 17], but also obtain some new formal solutions. The solutions obtained in this paper include polynomial, exponential, solitary wave, rational, triangular periodic, Jacobi and Weierstrass doubly periodic solutions.",

author = "Yong Chen and Qi Wang and Biao Li",

year = "2004",

month = nov,

doi = "10.1016/j.chaos.2004.02.024",

language = "英语",

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pages = "675--682",

journal = "Chaos, Solitons and Fractals",

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T1 - A generalized method and general form solutions to the Whitham-Broer-Kaup equation

AU - Chen, Yong

AU - Wang, Qi

AU - Li, Biao

PY - 2004/11

Y1 - 2004/11

N2 - Based on a more general transformation presented in this paper, a generalized method for finding more types travelling wave solutions of nonlinear evolution equations (NLEEs) is presented and implemented in a computer algebraic system. As an application of the method, Whitham-Broer-Kaup (WBK) equation is studied to illustrate the method. As a result, We cannot only successfully recover the previously known travelling wave solutions found by Fan's method [J. Phys. A 35 (2002) 6853; Comput. Phys. Commun. 53 (2003) 17], but also obtain some new formal solutions. The solutions obtained in this paper include polynomial, exponential, solitary wave, rational, triangular periodic, Jacobi and Weierstrass doubly periodic solutions.

AB - Based on a more general transformation presented in this paper, a generalized method for finding more types travelling wave solutions of nonlinear evolution equations (NLEEs) is presented and implemented in a computer algebraic system. As an application of the method, Whitham-Broer-Kaup (WBK) equation is studied to illustrate the method. As a result, We cannot only successfully recover the previously known travelling wave solutions found by Fan's method [J. Phys. A 35 (2002) 6853; Comput. Phys. Commun. 53 (2003) 17], but also obtain some new formal solutions. The solutions obtained in this paper include polynomial, exponential, solitary wave, rational, triangular periodic, Jacobi and Weierstrass doubly periodic solutions.

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DO - 10.1016/j.chaos.2004.02.024

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VL - 22

SP - 675

EP - 682

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

IS - 3

ER -

A generalized method and general form solutions to the Whitham-Broer-Kaup equation

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