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

2019 ◽  
Vol 94 ◽  
pp. 126-132 ◽  
Author(s):  
Zhongzhou Lan
Keyword(s):  
Fluid Dynamics ◽  
Variable Coefficient ◽  
Rogue Wave ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Rogue Wave Solutions ◽  
Dimensional Variable

Soliton interactions and Bäcklund transformation for a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili equation in fluid dynamics

2018 ◽  
Vol 32 (02) ◽  
pp. 1750170 ◽  
Author(s):  
Zi-Jian Xiao ◽  
Bo Tian ◽  
Yan Sun
Keyword(s):  
Fluid Dynamics ◽  
Shock Waves ◽  
Variable Coefficient ◽  
Bäcklund Transformation ◽  
Bilinear Forms ◽  
Backlund Transformation ◽  
Bell Polynomial ◽  
Soliton Interactions ◽  
Petviashvili Equation ◽  
Dimensional Variable

In this paper, we investigate a (2[Formula: see text]+[Formula: see text]1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili (mKP) equation in fluid dynamics. With the binary Bell-polynomial and an auxiliary function, bilinear forms for the equation are constructed. Based on the bilinear forms, multi-soliton solutions and Bell-polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton interactions are presented. Based on the graphic analysis, Parametric conditions for the existence of the shock waves, elevation solitons and depression solitons are given, and it is shown that under the condition of keeping the wave vectors invariable, the change of [Formula: see text] and [Formula: see text] can lead to the change of the solitonic velocities, but the shape of each soliton remains unchanged, where [Formula: see text] and [Formula: see text] are the variable coefficients in the equation. Oblique elastic interactions can exist between the (i) two shock waves, (ii) two elevation solitons, and (iii) elevation and depression solitons. However, oblique interactions between (i) shock waves and elevation solitons, (ii) shock waves and depression solitons are inelastic.

Rogue wave solutions, soliton and rogue wave mixed solution for a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation in fluids

2018 ◽  
Vol 32 (29) ◽  
pp. 1850358 ◽  
Author(s):  
Yu-Lan Ma ◽  
Bang-Qing Li
Keyword(s):  
Rogue Wave ◽  
Mixed Solution ◽  
Polynomial Functions ◽  
Nonlinear Wave Propagation ◽  
Bilinear Transformation ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Rogue Wave Solutions ◽  
Evolution Behavior ◽  
Hirota Bilinear

A generalized (3[Formula: see text]+[Formula: see text]1)-dimensional Kadomtsev–Petviashvili equation is investigated, which can be used to describe nonlinear wave propagation in fluids. Through choosing appropriate polynomial functions in bilinear form derived according Hirota bilinear transformation, one and two rogue wave solutions, and soliton and rogue wave mixed solution are constructed. Furthermore, based on the mixed solution, interaction and evolution behavior between the soliton and rogue wave is discussed. The result shows that the soliton will be gradually swallowing up the rogue wave with the increase of time. During the process, the energy carried by the rogue wave is absorbed by the soliton.

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