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.

Construction of lump-type and interaction solutions to an extended (3+1)-dimensional Jimbo–Miwa-like equation

2020 ◽  
Vol 34 (13) ◽  
pp. 2050130
Author(s):  
Feng-Hua Qi ◽  
Wen-Xiu Ma ◽  
Pan Wang ◽  
Qi-Xing Qu
Keyword(s):  
Wave Equations ◽  
Periodic Wave ◽  
Dynamical Theory ◽  
Periodic Waves ◽  
Bilinear Method ◽  
Interaction Solutions ◽  
Higher Dimensional ◽  
Kink Waves ◽  
Hirota Bilinear ◽  
Nonlinear Dispersive Wave

We present lump-type solutions and interaction solutions to an extended (3[Formula: see text]+[Formula: see text]1)-dimensional Jimbo–Miwa-like equation. Three classes of lump-type solutions are obtained by the Hirota bilinear method. Interaction solutions are among lump-type solutions, two kink waves and periodic waves, and between two kink waves and a periodic wave are computed. Dynamical characters of the obtained solutions are graphically exhibited. These wave solutions enrich the dynamical theory of higher-dimensional nonlinear dispersive wave equations.

Hybrid solutions of a (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation in an incompressible fluid

2021 ◽  
pp. 2150126
Author(s):  
Chong-Dong Cheng ◽  
Bo Tian ◽  
Cong-Cong Hu ◽  
Xin Zhao
Keyword(s):  
Incompressible Fluid ◽  
Bilinear Form ◽  
Periodic Wave ◽  
Incompressible Fluids ◽  
Ocean Engineering ◽  
Hybrid Solutions ◽  
Kink Wave ◽  
Kink Waves ◽  
Lump Wave

Incompressible fluids are studied in such disciplines as ocean engineering, astrophysics and aerodynamics. Under investigation in this paper is a [Formula: see text]-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation in an incompressible fluid. Based on the known bilinear form, BLMP hybrid solutions comprising a lump wave, a periodic wave and two kink waves, and hybrid solutions comprising a breather wave and multi-kink waves are derived. We observe the interaction among a lump wave, a periodic wave and two kink waves. Fission of a kink wave is observed: A kink wave divides into a breather wave and three kink waves. On the contrary, we see the fusion among a breather wave and three kink waves: The breather wave and three kink waves merge into a kink wave. Finally, we observe the interaction among a breather wave and four kink waves.

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.

Interaction Solutions for Lump-line Solitons and Lump-kink Waves of the Dimensionally Reduced Generalised KP Equation

2017 ◽  
Vol 72 (10) ◽  
pp. 955-961 ◽  
Author(s):  
Iftikhar Ahmed
Keyword(s):  
Nonlinear Phenomena ◽  
Kp Equation ◽  
The Third ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Contour Plots ◽  
Kink Wave ◽  
Kink Waves ◽  
Line Soliton ◽  
Interaction Phenomena

AbstractIn this work, we investigate dimensionally reduced generalised Kadomtsev-Petviashvili equation, which can describe many nonlinear phenomena in fluid dynamics. Based on the bilinear formalism, direct Maple symbolic computations are used with an ansätz function to construct three classes of interaction solutions between lump and line solitons. Furthermore, the dynamics of interaction phenomena is explained with 3D plots and 2D contour plots. For the first class of interaction solutions, lump appeared at t=0, and there was a normal interaction between lump and line solitons at t=1, 2, 5, and 10. For the second class of interaction solutions, lump appeared from one side of line soliton at t=0, but it started moving downward at t=1, 2, and 5. Finally, at t=10, this lump was completely swallowed by other side. By contrast, for the third class of interaction solutions, lump appeared from one side of line soliton at t=0, but it started moving upward at t=1, 2, and 5. Finally, at t=10, this lump was completely swallowed by other side. Furthermore, interaction solutions between lump solutions and kink wave are also investigated. These results might be helpful to understand the propagation processes for nonlinear waves in fluid mechanics.

Interaction Behaviours Between Soliton and Cnoidal Periodic Waves for the Cubic Generalised Kadomtsev–Petviashvili Equation

2015 ◽  
Vol 70 (7) ◽  
pp. 539-544 ◽  
Author(s):  
Bo Ren ◽  
Ji Lin
Keyword(s):  
Elliptic Integral ◽  
Elliptic Functions ◽  
Jacobi Elliptic Functions ◽  
Periodic Waves ◽  
The Third ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Kink Soliton

AbstractThe consistent tanh expansion (CTE) method is applied to the cubic generalised Kadomtsev–Petviashvili (CGKP) equation. The interaction solutions between one kink soliton and the cnoidal periodic waves are explicitly given. Some special concrete interaction solutions in terms of the Jacobi elliptic functions and the third type of incomplete elliptic integral are discussed both in analytical and graphical ways.

Interaction among a lump, periodic waves, and kink solutions to the KP-BBM equation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Junjie Li ◽  
Jalil Manafian ◽  
Nguyen Thi Hang ◽  
Dinh Tran Ngoc Huy ◽  
Alla Davidyants
Keyword(s):  
Soliton Solutions ◽  
Periodic Wave ◽  
Contour Plot ◽  
Periodic Waves ◽  
Hirota Bilinear Method ◽  
Algebraic Equations ◽  
Bilinear Method ◽  
Kink Wave ◽  
Hirota Bilinear ◽  
Bbm Equation

Abstract The Hirota bilinear method is prepared for searching the diverse soliton solutions to the (2+1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony (KP-BBM) equation. Also, the Hirota bilinear method is used to find the lump and interaction with two stripe soliton solutions. Interaction among lumps, periodic waves, and one-kink soliton solutions are investigated. Also, the solitary wave, periodic wave, and cross-kink wave solutions are examined for the KP-BBM equation. The graphs for various parameters are plotted to contain a 3D plot, contour plot, density plot, and 2D plot. We construct the exact lump and interaction among other types of solutions, by solving the underdetermined nonlinear system of algebraic equations with the associated parameters. Finally, analysis and graphical simulation are presented to show the dynamical characteristics of our solutions, and the interaction behaviors are revealed. The existing conditions are employed to discuss the available got solutions.

Interaction solutions of a variable-coefficient Kadomtsev–Petviashvili equation with self-consistent sources

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Na Yuan ◽  
Jian-Guo Liu ◽  
Aly R. Seadawy ◽  
Mostafa M. A. Khater
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Variable Coefficient ◽  
Periodic Wave ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Self Consistent ◽  
Contour Plots ◽  
Lump Wave ◽  
Interaction Phenomenon

Abstract Under investigation is a generalized variable-coefficient Kadomtsev–Petviashvili equation with self-consistent sources. Our main job is divided into four parts: (i) lump wave solution, (ii) interaction solutions between lump and solitary wave, (iii) breather wave solution and (iv) interaction solutions between lump and periodic wave. Furthermore, the interaction phenomenon of waves is shown in some 3D- and contour plots.

scholarly journals Application of Extended Rational Trigonometric Techniques to Investigate Solitary Wave Solutions

2021 ◽  
Author(s):  
Nadia Mahak ◽  
ghazala akram
Keyword(s):  
Exact Solutions ◽  
Traveling Wave Solutions ◽  
Analytical Techniques ◽  
Periodic Wave ◽  
Physical Activities ◽  
Solitary Wave Solutions ◽  
Geometrical Structures ◽  
Dark Solitons ◽  
Wave Solutions ◽  
Kink Wave

Abstract In this paper, a variety of novel exact traveling wave solutions are constructed for the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation via analytical techniques, namely, extended rational sine-cosine method and extended rational sinh-cosh method. The physical meaning of the geometrical structures for some of these solutions is discussed. Obtained solutions are expressed in terms of singular periodic wave, solitary waves, bright solitons, dark solitons, periodic wave and kink wave solutions with specific values of parameters. For the observation of physical activities of the problem, achieved exact solutions are vital. Moreover, to find analytical solutions of the proposed equation many methods have been used but given methodologies are effective, reliable and gave more and novel exact solutions.

New periodic wave, cross-kink wave and the interaction phenomenon for the Jimbo–Miwa-like equation

2019 ◽  
Vol 78 (3) ◽  
pp. 754-764 ◽  
Author(s):  
Runfa Zhang ◽  
Sudao Bilige ◽  
Tao Fang ◽  
Temuer Chaolu
Keyword(s):  
Periodic Wave ◽  
Kink Wave ◽  
Interaction Phenomenon

scholarly journals Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov-Kuznetsov Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Yun Wu ◽  
Zhengrong Liu
Keyword(s):  
Solitary Waves ◽  
Nonlinear Waves ◽  
Blow Up ◽  
Periodic Waves ◽  
The Third ◽  
Bifurcation Phenomena ◽  
Kink Waves ◽  
Fourth Kind

We study the bifurcation phenomena of nonlinear waves described by a generalized Zakharov-Kuznetsov equationut+au2+bu4ux+γuxxx+δuxyy=0. We reveal four kinds of interesting bifurcation phenomena. The first kind is that the low-kink waves can be bifurcated from the symmetric solitary waves, the 1-blow-up waves, the tall-kink waves, and the antisymmetric solitary waves. The second kind is that the 1-blow-up waves can be bifurcated from the periodic-blow-up waves, the symmetric solitary waves, and the 2-blow-up waves. The third kind is that the periodic-blow-up waves can be bifurcated from the symmetric periodic waves. The fourth kind is that the tall-kink waves can be bifurcated from the symmetric periodic waves.

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