scholarly journals Stripe solitons and lump solutions to a generalized (3 + 1)-dimensional B-type Kadomtsev-Petviashvili equation with variable coefficients in fluid dynamics

2021 ◽  
pp. 125198
Author(s):  
Wen-Hui Zhu ◽  
Jian-Guo Liu
Keyword(s):  
Fluid Dynamics ◽  
Variable Coefficients ◽  
Lump Solutions ◽  
Petviashvili Equation

Abundant Lump Solution and Interaction Phenomenon of (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation

2019 ◽  
Vol 20 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Jianqing Lü ◽  
Sudao Bilige ◽  
Xiaoqing Gao
Keyword(s):  
Symbolic Computation ◽  
Bilinear Form ◽  
Lump Solution ◽  
Lump Solutions ◽  
Interaction Solution ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Contour Plots ◽  
Special Case ◽  
Interaction Phenomenon

AbstractIn this paper, with the help of symbolic computation system Mathematica, six kinds of lump solutions and two classes of interaction solutions are discussed to the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation via using generalized bilinear form with a dependent variable transformation. Particularly, one special case are plotted as illustrative examples, and some contour plots with different determinant values are presented. Simultaneously, we studied the trajectory of the interaction solution.

Fission and fusion interaction phenomena of mixed lump kink solutions for a generalized (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

2018 ◽  
Vol 32 (15) ◽  
pp. 1850161 ◽  
Author(s):  
Yaqing Liu ◽  
Xiaoyong Wen
Keyword(s):  
Shallow Water ◽  
Symbolic Computation ◽  
Water Wave ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Lump Solutions ◽  
Shallow Water Wave ◽  
Petviashvili Equation ◽  
Kink Soliton ◽  
Interaction Phenomena

In this paper, a generalized (3[Formula: see text]+[Formula: see text]1)-dimensional B-type Kadomtsev–Petviashvili (gBKP) equation is investigated by using the Hirota’s bilinear method. With the aid of symbolic computation, some new lump, mixed lump kink and periodic lump solutions are derived. Based on the derived solutions, some novel interaction phenomena like the fission and fusion interactions between one lump soliton and one kink soliton, the fission and fusion interactions between one lump soliton and a pair of kink solitons and the interactions between two periodic lump solitons are discussed graphically. Results might be helpful for understanding the propagation of the shallow water wave.

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.

Lump solutions of a new generalized Kadomtsev–Petviashvili equation

2019 ◽  
Vol 33 (10) ◽  
pp. 1950126 ◽  
Author(s):  
Jing Yu ◽  
Wen-Xiu Ma ◽  
Shou-Ting Chen
Keyword(s):  
Differential Equation ◽  
Symbolic Computation ◽  
Transformation Formula ◽  
Lump Solutions ◽  
Petviashvili Equation ◽  
Free Parameters

A new generalized Kadomtsev–Petviashvili (GKP) equation is derived from a bilinear differential equation by taking the transformation [Formula: see text]. By symbolic computation with Maple, lump solutions, rationally localized in all directions in the space, to the GKP equation are presented. The obtained lump solutions contain a set of six free parameters, four of which should satisfy a nonzero determinant condition. As special examples, six particular lump solutions are constructed and depicted with [Formula: see text].

On a generalized Kadomtsev–Petviashvili equation with variable coefficients via symbolic computation

2007 ◽  
Vol 76 (5) ◽  
pp. 411-417 ◽  
Author(s):  
Li-Li Li ◽  
Bo Tian ◽  
Chun-Yi Zhang ◽  
Tao Xu
Keyword(s):  
Symbolic Computation ◽  
Variable Coefficients ◽  
Petviashvili Equation
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