scholarly journals New Generalized Soliton Solutions for a (3+1)-Dimensional Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
Yiren Chen
Keyword(s):  
Nonlinear Wave ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Hirota’S Method ◽  
Differentiable Functions ◽  
Wave Solutions ◽  
Simplified Hirota’S Method ◽  
Dimensional Equation ◽  
Hirota's Method ◽  
Nonlinear Wave Solutions

In this paper, we investigate the nonlinear wave solutions for a (3+1)-dimensional equation which can be reduced to the potential KdV equation. We present generalized N-soliton solutions in which some arbitrarily differentiable functions are involved by using a simplified Hirota’s method. Our work extends some previous results.

New (3+1)-dimensional nonlinear evolution equation: multiple soliton solutions

2014 ◽  
Vol 4 (4) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Multiple Soliton Solutions ◽  
Simplified Hirota’S Method ◽  
Hirota's Method

AbstractIn this work, we introduce an extended (3+1)-dimensional nonlinear evolution equation. We determine multiple soliton solutions by using the simplified Hirota’s method. In addition, we establish a variety of travelling wave solutions by using hyperbolic and trigonometric ansatze.

Multiple soliton solutions for the integrable couplings of the KdV and the KP equations

Open Physics ◽  
2013 ◽  
Vol 11 (3) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Hirota’S Method ◽  
Multiple Soliton Solutions ◽  
Simplified Hirota’S Method ◽  
Integrable Couplings ◽  
Kp Equations ◽  
Hirota's Method

AbstractIn this work, we study the nonlinear integrable couplings of the KdV and the Kadomtsev-Petviashvili (KP) equations. The simplified Hirota’s method will be used for this study. We show that these couplings possess multiple soliton solutions the same as the multiple soliton solutions of the KdV and the KP equations, but differ only in the coefficients of the transformation used. This difference exhibits soliton solutions for some equations and anti-soliton solutions for others.

A seventh-order member of KdV6 hierarchy and its (2+1)-dimensional extensions

2016 ◽  
Vol 30 (17) ◽  
pp. 1650198 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Dispersion Relations ◽  
Painlevé Analysis ◽  
Completely Integrable ◽  
Hirota’S Method ◽  
Multiple Soliton Solutions ◽  
Simplified Hirota’S Method ◽  
Seventh Order ◽  
Hirota's Method ◽  
Painleve Analysis

In this work, we investigate a completely integrable seventh-order member of the KdV6 hierarchy. We develop two extensions of (2[Formula: see text]+[Formula: see text]1) dimensions for this equation. We show that the dispersion relations are distinct that will reflect on the structures of the obtained solutions. We use the simplified Hirota’s method to determine multiple soliton solutions for these three equations. The integrability of the extended equations is tested by using the Painlevé analysis.

A new (3 + 1)-dimensional Painlevé-integrable Sakovich equation: multiple soliton solutions

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Design Methodology ◽  
Soliton Solutions ◽  
Complete Integrability ◽  
Content Type ◽  
Hirota’S Method ◽  
Multiple Soliton Solutions ◽  
Simplified Hirota’S Method ◽  
Hirota's Method ◽  
Practical Implications ◽  
Dispersion Term

Purpose This paper aims to develop a new (3 + 1)-dimensional Painlev´e-integrable extended Sakovich equation. This paper formally derives multiple soliton solutions for this developed model. Design/methodology/approach This paper uses the simplified Hirota’s method for deriving multiple soliton solutions. Findings This paper finds that the developed (3 + 1)-dimensional Sakovich model exhibits complete integrability in analogy with the standard Sakovich equation. Research limitations/implications This paper addresses the integrability features of this model via using the Painlev´e analysis. This paper reports multiple soliton solutions for this equation by using the simplified Hirota’s method. Practical implications The study reports three non-linear terms added to the standard Sakovich equation. Social implications The study presents useful algorithms for constructing new integrable equations and for handling these equations. Originality/value The paper reports a new Painlev´e-integrable extended Sakovich equation, which belongs to second-order partial differential equations. The constructed model does not contain any dispersion term such as uxxx.

Higher dimensional integrable Vakhnenko–Parkes equation: multiple soliton solutions

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Design Methodology ◽  
Soliton Solutions ◽  
Integrable Equation ◽  
Content Type ◽  
Hirota’S Method ◽  
Multiple Soliton Solutions ◽  
Simplified Hirota’S Method ◽  
Higher Dimensional ◽  
Hirota's Method ◽  
Practical Implications

Purpose This study aims to develop a new (3 + 1)-dimensional Painlevé-integrable extended Vakhnenko–Parkes equation. The author formally derives multiple soliton solutions for this developed model. Design/methodology/approach The study used the simplified Hirota’s method for deriving multiple soliton solutions. Findings The study finds that the developed (3 + 1)-dimensional Vakhnenko–Parkes model exhibits complete integrability in analogy with the standard Vakhnenko–Parkes equation. Research limitations/implications This study addresses the integrability features of this model via using the Painlevé analysis. The study also reports multiple soliton solutions for this equation by using the simplified Hirota’s method. Practical implications The work reports extension of the (1 + 1)-dimensional standard equation to a (3 + 1)-dimensional model. Social implications The work presents useful algorithms for constructing new integrable equations and for handling these equations. Originality/value The paper presents an original work with newly developed integrable equation and shows useful findings.

scholarly journals Nonlinear Wave Solutions of Cylindrical KdV-Burgers Equation in Nonextensive Plasmas for Astrophysical Objects

2020 ◽  
Vol 137 (6) ◽  
pp. 1061-1067
Author(s):  
U.M. Abdelsalam ◽  
M.S. Zobaer ◽  
H. Akther ◽  
M.G.M. Ghazal ◽  
M.M. Fares
Keyword(s):  
Nonlinear Wave ◽  
Burgers Equation ◽  
Wave Solutions ◽  
Astrophysical Objects ◽  
Nonlinear Wave Solutions

Resonance Y-type soliton, hybrid and quasi-periodic wave solutions of a generalized (2+1)-dimensional nonlinear wave equation

2021 ◽  
Author(s):  
Lingchao He ◽  
Jianwen Zhang ◽  
Zhonglong Zhao
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Water Waves ◽  
Asymptotic Properties ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Before And After

Abstract In this paper, we consider a generalized (2+1)-dimensional nonlinear wave equation. Based on the bilinear, the N-soliton solutions are obtained. The resonance Y-type soliton and the interaction solutions between M-resonance Y-type solitons and P-resonance Y-type solitons are constructed by adding some new constraints to the parameters of the N-soliton solutions. The new type of two-opening resonance Y-type soliton solutions are presented by choosing some appropriate parameters in 3-soliton solutions. The hybrid solutions consisting of resonance Y-type solitons, breathers and lumps are investigated. The trajectories of the lump waves before and after the collision with the Y-type solitons are analyzed from the perspective of mathematical mechanism. Furthermore, the multi-dimensional Riemann-theta function is employed to investigate the quasi-periodic wave solutions. The one-periodic and two-periodic wave solutions are obtained. The asymptotic properties are systematically analyzed, which establish the relations between the quasi-periodic wave solutions and the soliton solutions. The results may be helpful to provide some effective information to analyze the dynamical behaviors of solitons, fluid mechanics, shallow water waves and optical solitons.

scholarly journals Control of Nonlinear Wave Solutions to Neural Field Equations

2019 ◽  
Vol 18 (2) ◽  
pp. 1015-1036 ◽  
Author(s):  
Alexander Ziepke ◽  
Steffen Martens ◽  
Harald Engel
Keyword(s):  
Nonlinear Wave ◽  
Neural Field ◽  
Field Equations ◽  
Wave Solutions ◽  
Neural Field Equations ◽  
Nonlinear Wave Solutions
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