Lump and Lump–Kink Soliton Solutions of an Extended Boiti–Leon–Manna–Pempinelli Equation

2020 ◽  
Vol 21 (3-4) ◽  
pp. 371-377
Author(s):  
Han-Dong Guo ◽  
Tie-Cheng Xia
Keyword(s):  
Potential Function ◽  
Dynamic Characteristics ◽  
Soliton Solutions ◽  
Lump Solutions ◽  
3 Dimensional ◽  
Symbolic Computations ◽  
Interaction Solutions ◽  
Contour Plots ◽  
Kink Soliton

AbstractIn this paper, the extended Boiti–Leon–Manna–Pempinelli equation (eBLMP) is first proposed, and by Ma’s [1] method, a class of lump and lump–kink soliton solutions is explicitly generated by symbolic computations. The propagation orbit, velocity and extremum of the lump solutions on (x,y) plane are studied in detail. Interaction solutions composed of lump and kink soliton are derived by means of choosing appropriate real values on obtained parameter solutions. Furthermore, 3-dimensional plots, 2-dimensional curves, density plots and contour plots with particular choices of the involved parameters are depicted to demonstrate the dynamic characteristics of the presented lump and lump–kink solutions for the potential function v = 2ln( f(x))x.

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.

scholarly journals Abundant lump solutions and interaction solutions of a (3+1)-D Kadomtsev-Petviashvili equation

2019 ◽  
Vol 23 (4) ◽  
pp. 2437-2445 ◽  
Author(s):  
Xiaoqing Gao ◽  
Sudao Bilige ◽  
Jianqing Lü ◽  
Yuexing Bai ◽  
Runfa Zhang ◽  
...  
Keyword(s):  
Lump Solution ◽  
Solution Properties ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Lump Solutions ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Contour Plots ◽  
Hirota Bilinear

In this paper, abundant lump solutions and two types of interaction solutions of the (3+1)-D Kadomtsev-Petviashvili equation are obtained by the Hirota bilinear method. Some contour plots with different determinant values are sequentially given to show that the corresponding lump solution tends to zero when the deter-minant approaches to zero. The interaction solutions with special parameters are plotted to elucidate the solution properties.

Lump solitons and interaction phenomenon to a (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq-like equation

2019 ◽  
Vol 33 (32) ◽  
pp. 1950395 ◽  
Author(s):  
Na Liu ◽  
Yansheng Liu
Keyword(s):  
Symbolic Computation ◽  
Bilinear Form ◽  
Nonlinear Waves ◽  
Soliton Solutions ◽  
Lump Solutions ◽  
Interaction Solutions ◽  
Hirota’S Bilinear Form ◽  
Interaction Phenomenon

This paper studies lump solutions and interaction solutions for a (3[Formula: see text]+[Formula: see text]1)-dimensional Kadomtsev–Petviashvili–Boussinesq-like equation. With the help of symbolic computation and Hirota’s bilinear form, we obtain bright–dark lump solutions, lump-soliton solutions, and lump-kink solutions. Meanwhile, the dynamics of the obtained three classes of solutions are analyzed and exhibited mathematically and graphically. These results provide us with useful information to grasp the propagation processes of nonlinear waves.

Lump-type solutions, interaction solutions, and periodic lump solutions of the generalized (3+1)-dimensional Burgers equation

2020 ◽  
pp. 2150107
Author(s):  
Chun-Na Gao ◽  
Yun-Hu Wang
Keyword(s):  
Dynamic Characteristics ◽  
Wave Solution ◽  
Burgers Equation ◽  
Variable Transformation ◽  
Ansatz Method ◽  
Lump Solutions ◽  
Interaction Solutions ◽  
Bilinear Equation

In this paper, the lump-type solutions, interaction solutions, and periodic lump solutions of the generalized ([Formula: see text])-dimensional Burgers equation were obtained by using the ansatz method. Based on a variable transformation, the generalized ([Formula: see text])-dimensional Burgers equation was transformed into a bilinear equation. And then, lump-type solutions, two kinds of interaction solutions, and periodic lump solutions were obtained via solutions of the bilinear equation. Fission and fusion phenomena are found in the process of interaction between lump-type soliton and one stripe soliton, which can derive the lumpoff wave solution. The dynamic characteristics of these solutions were vividly displayed by graphics.

scholarly journals New Periodic Wave, Cross-Kink Wave, Breather, and the Interaction Phenomenon for the (2 + 1)-Dimensional Sharmo–Tasso–Olver Equation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Hongcai Ma ◽  
Caoyin Zhang ◽  
Aiping Deng
Keyword(s):  
Exact Solutions ◽  
Dynamic Characteristics ◽  
Periodic Wave ◽  
Periodic Waves ◽  
Trilinear Form ◽  
Interaction Solutions ◽  
Kink Wave ◽  
Kink Waves ◽  
Kink Soliton ◽  
Interaction Phenomenon

In this paper, with the aid of symbolic computation, several kinds of exact solutions including periodic waves, cross-kink waves, and breather are proposed by using a trilinear form for the (2 + 1)-dimensional Sharmo–Tasso–Olver equation. Then, by combing the different forms, the interactions between a lump and one-kink soliton and between a lump and periodic waves are generated. Moreover, the dynamic characteristics of interaction solutions are analyzed graphically by selecting suitable parameters with the help of Maple.

Interaction of localized waves and dynamic behavior in a (3 + 1)-dimensional partial differential equation

2020 ◽  
Vol 34 (21) ◽  
pp. 2050215
Author(s):  
Bo Ren ◽  
Ji Lin ◽  
Jun Yu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Three Dimensional ◽  
Linear Partial Differential Equation ◽  
Periodic Waves ◽  
Partial Differential ◽  
Ansatz Method ◽  
Lump Solutions ◽  
Contour Plots ◽  
Kink Soliton

A general third order of linear partial differential equation in [Formula: see text] dimensions is studied by using the ansätz method. The lump solutions which localize in all directions in the whole [Formula: see text]-space are derived by the ansätz method. Diversity interactions including interacted lumps with periodic waves, interaction between lumps and multi-soliton, and interaction among lumps, multi-soliton and periodic waves are obtained by selecting the arbitrary functions. The phenomena of interaction between a lump and one-kink soliton, interaction between a lump and periodic waves, and interaction among a lump, one-kink soliton and periodic waves are analyzed by the three-dimensional plots and contour plots. The results may enrich the existing lump solutions in the [Formula: see text]-dimensional partial differential equations.

scholarly journals Optical solitons and other soluions for Radhakrishnan–Kundu–Lakshmanan equation in birefringent fibers by an efficient computational technique

2021 ◽  
Author(s):  
M. Bilal ◽  
Mohammad Youins ◽  
Aly Ramadan Seadawy ◽  
S.T.R. Rizvi
Keyword(s):  
Soliton Solutions ◽  
Periodic Wave ◽  
Computational Technique ◽  
Mixed Complex ◽  
Symbolic Computations ◽  
Significant Relationships ◽  
Wave Solutions ◽  
Component Form ◽  
Contour Plots ◽  
Complex Phenomena

Abstract In this article, we are interested to discuss the exact optical soiltons and other solutions in birefringent fibers modeled by Radhakrishnan-Kundu-Lakshmanan equation in two component form for vector solitons. We extract the solutions in the form of hyperbolic, trigonometric and exponential functions including solitary wave solutions like multiple-optical soliton, mixed complex soliton solutions. The strategy that is used to explain the dynamics of soliton is known as generalized exponential rational function method. Moreover, singular periodic wave solutions are recovered and the constraint conditions for the existence of soliton solutions are also reported. Besides, the physical action of the solution attained are recorded in terms of 3D, 2D and contour plots for distinct parameters. The achieved outcomes show that the applied computational strategy is direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations. The primary benefit of this technique is to develop a significant relationships between NLPDEs and others simple NLODEs and we have succeeded in a single move to get and organize various types of new solutions. The obtained outcomes show that the applied method is concise, direct, elementary and can be imposed in more complex phenomena with the assistant of symbolic computations

Mixed lump-solitons, periodic lump and breather soliton solutions for (2 + 1)-dimensional extended Kadomtsev–Petviashvili dynamical equation

2019 ◽  
Vol 33 (05) ◽  
pp. 1950019 ◽  
Author(s):  
Iftikhar Ahmed ◽  
Aly R. Seadawy ◽  
Dianchen Lu
Keyword(s):  
Symbolic Computation ◽  
Dynamical Equation ◽  
Soliton Solutions ◽  
Hirota Bilinear Method ◽  
Kp Equation ◽  
Bilinear Method ◽  
Lump Solutions ◽  
Contour Plots ◽  
Hirota Bilinear

In this study, based on the Hirota bilinear method, mixed lump-solitons, periodic lump and breather soliton solutions are derived for (2 + 1)-dimensional extended KP equation with the aid of symbolic computation. Furthermore, dynamics of these solutions are explained with 3d plots and 2d contour plots by taking special choices of the involved parameters. Through the mixed lump-soliton solutions, we observe two fusion phenomena, first from interaction of lump and single soliton and other from interaction of lump with two solitons. In both cases, lump moves gradually towards soliton and transfers energy until it completely merges with the solitons. We also observe new characteristics of periodic lump solutions and kinky breather solitons.

New integrable (2+1)- and (3+1)-dimensional shallow water wave equations: multiple soliton solutions and lump solutions

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Shallow Water ◽  
Water Wave ◽  
Wave Equations ◽  
Soliton Solutions ◽  
Lump Solutions ◽  
Content Type ◽  
Shallow Water Wave ◽  
Multiple Soliton Solutions ◽  
Simplified Hirota’S Method ◽  
Shallow Water Wave Equations

Purpose This study aims to develop two integrable shallow water wave equations, of higher-dimensions, and with constant and time-dependent coefficients, respectively. The author derives multiple soliton solutions and a class of lump solutions which are rationally localized in all directions in space. Design/methodology/approach The author uses the simplified Hirota’s method and lump technique for determining multiple soliton solutions and lump solutions as well. The author shows that the developed (2+1)- and (3+1)-dimensional models are completely integrable in in the Painlené sense. Findings The paper reports new Painlevé-integrable extended equations which belong to the shallow water wave medium. Research limitations/implications The author addresses the integrability features of this model via using the Painlevé analysis. The author reports multiple soliton solutions for this equation by using the simplified Hirota’s method. Practical implications The obtained lump solutions include free parameters; some parameters are related to the translation invariance and the other parameters satisfy a non-zero determinant condition. Social implications The work presents useful algorithms for constructing new integrable equations and for the determination of lump solutions. Originality/value The paper presents an original work with newly developed integrable equations and shows useful findings of solitary waves and lump solutions.

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