# Bilinearization and new soliton solutions of Whitham-Broer-Kaup equations with time-dependent coefficients

Volume 10, Issue 5, pp 2324--2339 Publication Date: May 22, 2017       Article History
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### Authors

Sheng Zhang - School of Mathematics and Physics, Bohai University, Jinzhou 121013, China.
Zhaoyu Wang - School of Mathematics and Physics, Bohai University, Jinzhou 121013, China.

### Abstract

In this paper, Whitham–Broer–Kaup (WBK) equations with time-dependent coefficients are exactly solved through Hirota’s bilinear method. To be specific, the WBK equations are first reduced into a system of variable-coefficient Ablowitz–Kaup– Newell–Segur (AKNS) equations. With the help of the AKNS equations, bilinear forms of the WBK equations are then given. Based on a special case of the 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 graphically shown that the dynamical evolutions of the obtained one-, two- and three-soliton solutions possess time-varying amplitudes in the process of propagations.

### Keywords

• Bilinear form
• soliton solution
• WKB equations with time-dependent coefficients
• Hirota’s bilinear method.

•  35Q51
•  35Q53
•  35Q99

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