scholarly journals Painlevé Analysis, Soliton Molecule, and Lump Solution of the Higher-Order Boussinesq Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Bo Ren
Keyword(s):  
Bilinear Form ◽  
Boussinesq Equation ◽  
Higher Order ◽  
Lump Solution ◽  
Painlevé Analysis ◽  
Resonance Mechanism ◽  
Variable Transformation ◽  
Localized Excitations ◽  
Lump Wave ◽  
Multisoliton Solutions

The Painlevé integrability of the higher-order Boussinesq equation is proved by using the standard Weiss-Tabor-Carnevale (WTC) method. The multisoliton solutions of the higher-order Boussinesq equation are obtained by introducing dependent variable transformation. The soliton molecule and asymmetric soliton of the higher-order Boussinesq equation can be constructed by the velocity resonance mechanism. Lump solution can be derived by solving the bilinear form of the higher-order Boussinesq equation. By some detailed calculations, the lump wave of the higher-order Boussinesq equation is just the bright form. These types of the localized excitations are exhibited by selecting suitable parameters.

scholarly journals Characteristics of the Soliton Molecule and Lump Solution in the 2 + 1 -Dimensional Higher-Order Boussinesq Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Bo Ren
Keyword(s):  
Bound States ◽  
Boussinesq Equation ◽  
Rational Solution ◽  
Quadratic Function ◽  
Special Kind ◽  
Higher Order ◽  
Lump Solution ◽  
Resonance Mechanism ◽  
Lump Wave ◽  
Nonlinear Wave Field

The soliton molecules, as bound states of solitons, have attracted considerable attention in several areas. In this paper, the 2 + 1 -dimensional higher-order Boussinesq equation is constructed by introducing two high-order Hirota operators in the usual 2 + 1 -dimensional Boussinesq equation. By the velocity resonance mechanism, the soliton molecule and the asymmetric soliton of the higher-order Boussinesq equation are constructed. The soliton molecule does not exist for the usual 2 + 1 -dimensional Boussinesq equation. As a special kind of rational solution, the lump wave is localized in all directions and decays algebraically. The lump solution of the higher-order Boussinesq equation is obtained by using a quadratic function. This lump wave is just the bright form by some detail analysis. The graphics in this study are carried out by selecting appropriate parameters. The results in this work may enrich the variety of the dynamics of the high-dimensional nonlinear wave field.

scholarly journals Studying Lump solutions, Rogue wave solutions and dynamical interaction for new model generating from lax pair

2020 ◽  
Vol 15 ◽  
pp. 67
Author(s):  
M. K. Elboree
Keyword(s):  
Bilinear Form ◽  
Rogue Wave ◽  
Dynamical Behavior ◽  
Elastic Interaction ◽  
Lax Pair ◽  
Lump Solution ◽  
Dynamical Interaction ◽  
Wave Solutions ◽  
Rogue Wave Solutions ◽  
Lump Wave

In this paper, we consider the (3 + 1)-dimensional Burgers-like equation which arises in fluid mechanics, which constructed from Lax pair generating technique. The bilinear form for this model is obtained to construct the multiple-kink solutions. Lump solution, rogue wave solutions are constructed via the obtained bilinear form for this model. The physical phenomena for these solution are analyzed by studying the influence of the parameters for these solutions. The phase shifts, propagation directions and amplitudes for these solutions are controlled via these parameters. The collisions between the lump wave and the stripe soliton, which is called lumpoff solution are completely non-elastic interaction. Finally, the figures of the solutions are shown to study the dynamical behavior for the lump, rogue wave and the properties of the interaction phenomena under various parameters for (3 + 1)-dimensional Burgers-like equation. These results can’t be found in the previous scientific papers.

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.

Lump and interactional solutions of the (2+1)-dimensional generalized breaking soliton equation

2019 ◽  
Vol 34 (03) ◽  
pp. 2050037
Author(s):  
Yu-Pei Fan ◽  
Ai-Hua Chen
Keyword(s):  
Solitary Wave ◽  
Asymptotic Analysis ◽  
Bilinear Form ◽  
Lump Solution ◽  
Soliton Equation ◽  
Long Wave ◽  
Wave Limit

In this paper, by using the long wave limit method, we study lump solution and interactional solution of the (2[Formula: see text]+[Formula: see text]1)-dimensional generalized breaking soliton equation without using bilinear form. The moving properties of the lump solution, and the interactional properties of a lump and a solitary wave, are analyzed theoretically and graphically with asymptotic analysis.

scholarly journals Multiple Lump Solutions of the (4+1)-Dimensional Fokas Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Hongcai Ma ◽  
Yunxiang Bai ◽  
Aiping Deng
Keyword(s):  
Symbolic Computation ◽  
Bilinear Form ◽  
Three Dimensional ◽  
Structural Features ◽  
Computation Method ◽  
Lump Solutions ◽  
Wave Solutions ◽  
Lump Wave

In this paper, we investigate multiple lump wave solutions of the new (4+1)-dimensional Fokas equation by adopting a symbolic computation method. We get its 1-lump solutions, 3-lump solutions, and 6-lump solutions by using its bilinear form. Moreover, some basic characters and structural features of multiple lump waves are explained by depicting the three-dimensional plots.

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