Periodic, breather and rogue wave solutions for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation in fluid dynamics

Abstract Under investigation in this paper is a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation, which describes the propagation of nonlinear waves in fluid dynamics. Periodic wave solutions are constructed by virtue of the Hirota–Riemann method. Based on the extended homoclinic test approach, breather and rogue wave solutions are obtained. Moreover, through the symbolic computation, the relationship between the one-periodic wave solutions and one-soliton solutions has been analytically discussed, and it is shown that the one-periodic wave solutions approach the one-soliton solutions when the amplitude η → 0 .

[1]  Bo Tian,et al.  Bäcklund transformations and soliton solutions for a $$(3+1)$$(3+1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics , 2015 .

[2]  Gao-Qing Meng,et al.  Double Wronskian Solutions for a Generalized Nonautonomous Nonlinear Equation in a Nonlinear Inhomogeneous Fiber , 2018, Communications in Theoretical Physics.

[3]  Yi-Tian Gao,et al.  Solitons and Bäcklund transformation for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation in fluid dynamics , 2016, Appl. Math. Lett..

[4]  R. Grimshaw,et al.  Internal solitary wave generation by tidal flow over topography , 2017, Journal of Fluid Mechanics.

[5]  Bo Tian,et al.  Rogue waves and lump solutions for a (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation in fluid mechanics , 2017 .

[6]  Gao-Qing Meng,et al.  Dark solitons for the (2+1)-dimensional Davey–Stewartson-like equations in the electrostatic wave packets , 2018 .

[7]  Wenxiu Ma,et al.  Lump solutions to the Kadomtsev–Petviashvili equation , 2015 .

[8]  C. M. Khalique,et al.  Exact solutions and conservation laws of a (3+1)-dimensional B-type Kadomtsev-Petviashvili equation , 2013, Advances in Difference Equations.

[9]  Abdul-Majid Wazwaz,et al.  Two forms of (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation: multiple soliton solutions , 2012 .

[10]  Xin-Yi Gao Bäcklund transformation and shock-wave-type solutions for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation in fluid mechanics , 2015 .

[11]  Gao-Qing Meng,et al.  Collisions between the dark solitons for a nonlinear system in the geophysical fluid , 2018 .

[12]  Yi-Tian Gao,et al.  Periodic wave, breather wave and travelling wave solutions of a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation in fluids or plasmas , 2016 .

[13]  Da-Wei Zuo,et al.  Multi-Soliton Solutions of the Generalized Sawada–Kotera Equation , 2016 .

[14]  Yi-Tian Gao,et al.  Inelastic interactions of the multiple-front waves for the modified Kadomtsev–Petviashvili equation in fluid dynamics, plasma physics and electrodynamics , 2009 .

[15]  Bo Tian,et al.  Solitons and rouge waves for a generalized (3+1)-dimensional variable-coefficient Kadomtsev-Petviashvili equation in fluid mechanics , 2016, Comput. Math. Appl..

[16]  Yi-Tian Gao,et al.  Bilinear Bäcklund transformation, soliton and periodic wave solutions for a $$\varvec{(3 + 1)}$$(3+1)-dimensional variable-coefficient generalized shallow water wave equation , 2017 .

[17]  Osborne,et al.  Soliton basis states in shallow-water ocean surface waves. , 1991, Physical review letters.

[18]  Shou-Fu Tian,et al.  Riemann theta functions periodic wave solutions and rational characteristics for the nonlinear equations , 2010 .