Nonautonomous lump solutions for a variable–coefficient Kadomtsev–Petviashvili equation

2021 ◽  
Vol 119 ◽  
pp. 107201
Author(s):  
Yun-Hu Wang
Keyword(s):  
Variable Coefficient ◽  
Lump Solutions ◽  
Petviashvili Equation

Rational solutions and lump solutions to a non-isospectral and generalized variable-coefficient Kadomtsev–Petviashvili equation

2018 ◽  
Vol 95 (2) ◽  
pp. 1027-1033 ◽  
Author(s):  
Jian-Guo Liu ◽  
Mostafa Eslami ◽  
Hadi Rezazadeh ◽  
Mohammad Mirzazadeh
Keyword(s):  
Variable Coefficient ◽  
Rational Solutions ◽  
Lump Solutions ◽  
Petviashvili Equation

scholarly journals Lump solutions for the dimensionally reduced variable coefficient B-type Kadomtsev-Petviashvili equation

2021 ◽  
pp. 39-39
Author(s):  
Yanni Zhang ◽  
Xin Zhao ◽  
Jing Pang
Keyword(s):  
Nonlinear Equations ◽  
Present Method ◽  
Variable Coefficient ◽  
Solution Process ◽  
Solution Properties ◽  
Lump Solutions ◽  
Petviashvili Equation ◽  
Bilinear Formulation ◽  
Hirota Bilinear

Based on Hirota bilinear formulation, the lump solutions to dimensionally reduced generalized variable coefficient B-type Kadomtsev-Petviashvili equation are obtained. The solution process is figured out and the solution properties are illustrated graphically. The present method can be extended to other nonlinear equations.

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.

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].

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