Wronskian and Grammian determinant structure solutions for a variable-coefficient forced Kadomtsev–Petviashvili equation in fluid dynamics

2014 ◽  
Vol 413 ◽  
pp. 635-642 ◽  
Author(s):  
Xiang-Hua Meng
Keyword(s):  
Fluid Dynamics ◽  
Variable Coefficient ◽  
Petviashvili Equation ◽  
Determinant Structure ◽  
Grammian Determinant

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.

Wronskian and Grammian Determinant Solutions for a Variable-Coefficient Kadomtsev–Petviashvili Equation

2008 ◽  
Vol 49 (5) ◽  
pp. 1125-1128 ◽  
Author(s):  
Yao Zhen-Zhi ◽  
Zhang Chun-Yi ◽  
Zhu Hong-Wu ◽  
Meng Xiang-Hua ◽  
Lü Xing ◽  
...  
Keyword(s):  
Variable Coefficient ◽  
Petviashvili Equation ◽  
Grammian Determinant

Multiwave interaction solutions for a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wenying Cui ◽  
Yinping Liu ◽  
Zhibin Li
Keyword(s):  
Fluid Dynamics ◽  
Algebraic Method ◽  
Higher Order ◽  
Decomposition Algorithm ◽  
Periodic Waves ◽  
Order Interaction ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Bkp Equation ◽  
Interaction Phenomena

Abstract In this paper, a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation is investigated and its various new interaction solutions among solitons, rational waves and periodic waves are obtained by the direct algebraic method, together with the inheritance solving technique. The results are fantastic interaction phenomena, and are shown by figures. Meanwhile, any higher order interaction solutions among solitons, breathers, and lump waves are constructed by an N-soliton decomposition algorithm developed by us. These innovative results greatly enrich the structure of the solutions of this equation.

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