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On periodic wave solutions with asymptotic behaviors to a (3+1)(3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation in fluid dynamics ☆

Research paper by Jian-Min Tu, Shou-Fu Tian, Mei-Juan Xu, Pan-Li Ma, Tian-Tian Zhang

Indexed on: 09 Oct '16Published on: 20 Sep '16Published in: Computers & Mathematics with Applications



Abstract

In this paper, a (3+1)(3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation is investigated, which can be used to describe weakly dispersive waves propagating in a quasi media and fluid mechanics. Based on the Bell polynomials, its multiple-soliton solutions and the bilinear form with some reductions are derived, respectively. Furthermore, by using Riemann theta function, we construct one- and two-periodic wave solutions for the equation. Finally, we study the asymptotic behavior of the periodic wave solutions, which implies that the periodic wave solutions can be degenerated to the soliton solutions under a small amplitude limit.

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