**Volume 10, Issue 5, pp 2324--2339**

**Publication Date**: 2017-05-22

http://dx.doi.org/10.22436/jnsa.010.05.05

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

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

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.

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

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