1-Soliton solutions of complex modified KdV equation with time-dependent coefficients

2013 ◽  
Vol 87 (9) ◽  
pp. 909-912 ◽  
Author(s):  
H. Kumar ◽  
F. Chand
Keyword(s):  
Kdv Equation ◽  
Soliton Solutions ◽  
Time Dependent ◽  
Modified Kdv Equation

EXACT SOLITON SOLUTIONS AND QUASI-PERIODIC WAVE SOLUTIONS TO THE FORCED VARIABLE-COEFFICIENT KdV EQUATION

2012 ◽  
Vol 26 (19) ◽  
pp. 1250072 ◽  
Author(s):  
YI ZHANG ◽  
ZHILONG CHENG
Keyword(s):  
Variable Coefficient ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Time Dependent ◽  
Bilinear Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Hirota Bilinear ◽  
Exact Soliton Solutions

In this paper, the time-dependent variable-coefficient KdV equation with a forcing term is considered. Based on the Hirota bilinear method, the bilinear form of this equation is obtained, and the multi-soliton solutions are studied. Then the periodic wave solutions are obtained by using Riemann theta function, and it is also shown that classical soliton solutions can be reduced from the periodic wave solutions.

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
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