THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Sheng Zhang

,

Mingying Liu

,

Bo Xu

NEW MULTI-SOLITON SOLUTIONS OF WHITHAM-BROER-KAUP SHALLOW-WATER-WAVE EQUATIONS

ABSTRACT
In this paper, new and more general Whitham-Broer-Kaup equations which can describe the propagation of shallow-water waves are exactly solved in the framework of Hirota's bilinear method and new multi-soliton solutions are obtained. To be specific, the Whitham-Broer-Kaup equations are first reduced into Ablowitz- Kaup-Newell-Segur equations. With the help of this equations, bilinear forms of the Whitham-Broer-Kaup equations are then derived. Based on the derived bilinear forms, new one-soliton solutions, two-soliton solutions, three-soliton solutions, and the uniform formulae of n-soliton solutions are finally obtained. It is shown that adopting the bilinear forms without loss of generality play a key role in obtaining these new multi-soliton solutions.
KEYWORDS
Whitham-Broer-Kaup equations, Ablowitz-Kaup-Newell-Segurequations, Hirota’s bilinear method, Bilinear forms, soliton solution
PAPER SUBMITTED: 2017-04-12
PAPER REVISED: 2017-05-17
PAPER ACCEPTED: 2017-05-25
PUBLISHED ONLINE: 2017-12-02
DOI REFERENCE: https://doi.org/10.2298/TSCI17S1137Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Supplement 1, PAGES [S137 - S144]
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New multi-soliton solutions of Whitham-Broer-Kaup shallow-water-wave equations

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