Extended KP equations and extended system of KP equations: multiple-soliton solutions

2011 ◽  
Vol 89 (7) ◽  
pp. 739-743 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Dispersion Relations ◽  
Kp Equation ◽  
Extended System ◽  
Multiple Soliton Solutions ◽  
Simplified Method ◽  
Kp Equations

In this work we study an extended Kadomtsev–Petviashvili (KP) equation and a system of KP equations. We show that the extension terms do not kill the integrability of typical models. Hereman’s simplified method is used to justify this goal. Multiple soliton solutions will be derived for each model. The analysis highlights the effects of the extension terms on the dispersion relations, and hence on the structures of the solutions.

Two integrable extensions of the Kadomtsev-Petviashvili equation

Open Physics ◽  
2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Kp Equation ◽  
Completely Integrable ◽  
Multiple Soliton Solutions ◽  
Petviashvili Equation ◽  
Singular Soliton ◽  
Multiple Singular Soliton Solutions

AbstractIn this work, two new completely integrable extensions of the Kadomtsev-Petviashvili (eKP) equation are developed. Multiple soliton solutions and multiple singular soliton solutions are derived to demonstrate the compatibility of the extensions of the KP equation.

Multiple-soliton solutions for coupled KdV and coupled KP systems

2009 ◽  
Vol 87 (12) ◽  
pp. 1227-1232 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Resonance Phenomenon ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Multiple Soliton Solutions ◽  
Two Systems ◽  
Kp Equations ◽  
Hirota Bilinear ◽  
Singular Soliton ◽  
Multiple Singular Soliton Solutions

In this work we study two systems of coupled KdV and coupled KP equations. The Hirota bilinear method is applied to show that these two systems are completely integrable. Multiple-soliton solutions and multiple singular-soliton solutions are derived for each system. The resonance phenomenon is examined as well.

Multiple-soliton solutions and lumps of a (3+1)-dimensional generalized KP equation

2018 ◽  
Vol 95 (2) ◽  
pp. 1687-1692 ◽  
Author(s):  
Jianping Yu ◽  
Fudong Wang ◽  
Wenxiu Ma ◽  
Yongli Sun ◽  
Chaudry Masood Khalique
Keyword(s):  
Soliton Solutions ◽  
Kp Equation ◽  
Multiple Soliton Solutions ◽  
Generalized Kp Equation

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.

One and two soliton solutions for seventh-order Caudrey-Dodd-Gibbon and Caudrey-Dodd-Gibbon-KP equations

Open Physics ◽  
2012 ◽  
Vol 10 (4) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Kp Equation ◽  
Bilinear Method ◽  
Seventh Order ◽  
Kp Equations ◽  
Simplified Form

AbstractIn this work, we explore more applications of the simplified form of the bilinear method to the seventhorder Caudrey-Dodd-Gibbon (CDG) and the Caudrey-Dodd-Gibbon-KP (CDG-KP) equation. We formally derive one and two soliton solutions for each equation. We also show that the two equations do not show resonance.

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.

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