Geodesic
Bilinearization and new soliton solutions of Whitham-Broer-Kaup equations with time-dependent coefficients
Zhang, Sheng1 ; Wang, Zhaoyu1
1 School of Mathematics and Physics, Bohai University, Jinzhou 121013, China
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 5, p. 2324-2339.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.010.05.05
Classification : 35Q51, 35Q53, 35Q99
Keywords: Bilinear form, soliton solution, WKB equations with time-dependent coefficients, Hirota’s bilinear method.

Zhang, Sheng 1 ; Wang, Zhaoyu 1

1 School of Mathematics and Physics, Bohai University, Jinzhou 121013, China 
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Zhang, Sheng; Wang, Zhaoyu. Bilinearization and new soliton solutions of Whitham-Broer-Kaup equations with time-dependent coefficients. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 5, p. 2324-2339. doi : 10.22436/jnsa.010.05.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.05.05/

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