scholarly journals A two-mode modified KdV equation with multiple soliton solutions

2017 ◽  
Vol 70 ◽  
pp. 1-6 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Kdv Equation ◽  
Soliton Solutions ◽  
Multiple Soliton Solutions ◽  
Modified Kdv Equation

Integrability of coupled KdV equations

Open Physics ◽  
2011 ◽  
Vol 9 (3) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Kdv Equation ◽  
Soliton Solutions ◽  
Resonance Phenomenon ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Kdv Equations ◽  
Multiple Soliton Solutions ◽  
Coupled Kdv Equations ◽  
Singular Soliton ◽  
Multiple Singular Soliton Solutions

AbstractThe integrability of coupled KdV equations is examined. The simplified form of Hirota’s bilinear method is used to achieve this goal. Multiple-soliton solutions and multiple singular soliton solutions are formally derived for each coupled KdV equation. The resonance phenomenon of each model will be examined.

Higher-order rational soliton solutions for the fifth-order modified KdV and KdV equations

2021 ◽  
pp. 2150036
Author(s):  
Zhi-Jie Pei ◽  
Hai-Qiang Zhang
Keyword(s):  
Darboux Transformation ◽  
Fourth Order ◽  
Taylor Expansion ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Higher Order ◽  
Kdv Equations ◽  
Perturbation Formula ◽  
Modified Kdv Equation ◽  
Fifth Order

In this paper, we construct the generalized perturbation ([Formula: see text], [Formula: see text])-fold Darboux transformation of the fifth-order modified Korteweg-de Vries (KdV) equation by the Taylor expansion. We use this transformation to derive the higher-order rational soliton solutions of the fifth-order modified KdV equation. We find that these higher-order rational solitons admit abundant interaction structures. We graphically present the dynamics behaviors from the first- to fourth-order rational solitons. Furthermore, by the Miura transformation, we obtain the complex rational soliton solutions of the fifth-order KdV equation.

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