THERMAL SCIENCE

International Scientific Journal

Sheng ZhangORCID

,

Mingying Liu

,

Bo XuORCID

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, PAGES [137 - 144]
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New multi-soliton solutions of Whitham-Broer-Kaup shallow-water-wave equations

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence