TheN-Soliton Solutions for the Modified KdV Equation with Self-Consistent Sources

2002 ◽  
Vol 71 (11) ◽  
pp. 2649-2656 ◽  
Author(s):  
Da-jun Zhang
Keyword(s):  
Kdv Equation ◽  
Soliton Solutions ◽  
Modified Kdv Equation ◽  
Self Consistent

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.

N -Soliton Solutions of Modified KdV Equation under Bargmann Constraint

2010 ◽  
Vol 54 (1) ◽  
pp. 21-26
Author(s):  
Ou Mei-Ying ◽  
Zhai Wen ◽  
Chen Deng-Yuan
Keyword(s):  
Kdv Equation ◽  
Soliton Solutions ◽  
Modified Kdv Equation

The bound-state soliton solutions of the complex modified KdV equation

2020 ◽  
Vol 36 (6) ◽  
pp. 065003 ◽  
Author(s):  
Yongshuai Zhang ◽  
Xiangxing Tao ◽  
Shuwei Xu
Keyword(s):  
Kdv Equation ◽  
Soliton Solutions ◽  
Bound State ◽  
Modified Kdv Equation

The periodic solutions of the discrete modified KdV equation with a self-consistent source

2020 ◽  
Vol 376 ◽  
pp. 125136
Author(s):  
Aygul Babadjanova ◽  
Thomas Kriecherbauer ◽  
Gayrat Urazboev
Keyword(s):  
Periodic Solutions ◽  
Kdv Equation ◽  
Modified Kdv Equation ◽  
Self Consistent
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