Soliton solutions for a second-order KdV equation

1994 ◽  
Vol 185 (2) ◽  
pp. 174-176 ◽  
Author(s):  
Sergei V. Korsunsky
Keyword(s):  
Kdv Equation ◽  
Soliton Solutions ◽  
Second Order

THE SECOND-ORDER KdV EQUATION AND ITS SOLITON-LIKE SOLUTION

2009 ◽  
Vol 23 (14) ◽  
pp. 1771-1780 ◽  
Author(s):  
CHUN-TE LEE ◽  
JINN-LIANG LIU ◽  
CHUN-CHE LEE ◽  
YAW-HONG KANG
Keyword(s):  
Solitary Waves ◽  
Soliton Solution ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Second Order ◽  
Close Resemblance ◽  
De Vries

This paper presents both the theoretical and numerical explanations for the existence of a two-soliton solution for a second-order Korteweg-de Vries (KdV) equation. Our results show that there exists "quasi-soliton" solutions for the equation in which solitary waves almost retain their identities in a suitable physical regime after they interact, and bear a close resemblance to the pure KdV solitons.

Multi-Soliton and Rational Solutions for the Extended Fifth-Order KdV Equation in Fluids

2015 ◽  
Vol 70 (7) ◽  
pp. 559-566 ◽  
Author(s):  
Gao-Qing Meng ◽  
Yi-Tian Gao ◽  
Da-Wei Zuo ◽  
Yu-Jia Shen ◽  
Yu-Hao Sun ◽  
...  
Keyword(s):  
Kdv Equation ◽  
Soliton Solutions ◽  
Second Order ◽  
Wave Shape ◽  
Rational Solutions ◽  
Weakly Nonlinear ◽  
First Order ◽  
Propagation Properties ◽  
Kdv Type Equations ◽  
Fifth Order

AbstractKorteweg–de Vries (KdV)-type equations are used as approximate models governing weakly nonlinear long waves in fluids, where the first-order nonlinear and dispersive terms are retained and in balance. The retained second-order terms can result in the extended fifth-order KdV equation. Through the Darboux transformation (DT), multi-soliton solutions for the extended fifth-order KdV equation with coefficient constraints are constructed. Soliton propagation properties and interactions are studied: except for the velocity, the amplitude and width of the soliton are not influenced by the coefficient of the original equation; the amplitude, velocity, and wave shape of each soltion remain unchanged after the interaction. By virtue of the generalised DT and Taylor expansion of the solutions for the corresponding Lax pair, the first- and second-order rational solutions of the equation are obtained.

Multi-soliton solutions and Bäcklund transformation for a two-mode KdV equation in a fluid

2016 ◽  
Vol 27 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Zi-Jian Xiao ◽  
Bo Tian ◽  
Hui-Ling Zhen ◽  
Jun Chai ◽  
Xiao-Yu Wu
Keyword(s):  
Bäcklund Transformation ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Backlund Transformation

Soliton solutions to KdV equation with spatio-temporal dispersion

2016 ◽  
Vol 114 ◽  
pp. 192-203 ◽  
Author(s):  
Houria Triki ◽  
Turgut Ak ◽  
Seithuti Moshokoa ◽  
Anjan Biswas
Keyword(s):  
Kdv Equation ◽  
Soliton Solutions ◽  
Spatio Temporal ◽  
Temporal Dispersion

New Dark Soliton Solutions of the KdV Equation

1993 ◽  
Vol 20 (4) ◽  
pp. 493-493
Author(s):  
Zong-Yun Chen ◽  
Nian-Ning Huang
Keyword(s):  
Kdv Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
The Kdv Equation

scholarly journals Solutions of the perturbed KdV equation for convecting fluids by factorizations

Open Physics ◽  
2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Octavio Cornejo-Pérez ◽  
Haret Rosu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Kdv Equation ◽  
Travelling Wave ◽  
Second Order ◽  
Travelling Wave Solutions ◽  
Second Order Differential Equation ◽  
Wave Solutions ◽  
Perturbed Kdv Equation

AbstractIn this paper, we obtain some new explicit travelling wave solutions of the perturbed KdV equation through recent factorization techniques that can be performed when the coefficients of the equation fulfill a certain condition. The solutions are obtained by using a two-step factorization procedure through which the perturbed KdV equation is reduced to a nonlinear second order differential equation, and to some Bernoulli and Abel type differential equations whose solutions are expressed in terms of the exponential andWeierstrass functions.

scholarly journals Soliton Solutions of a Generalized Discrete KdV Equation

2012 ◽  
Vol 81 (8) ◽  
pp. 084002 ◽  
Author(s):  
Masataka Kanki ◽  
Jun Mada ◽  
Tetsuji Tokihiro
Keyword(s):  
Kdv Equation ◽  
Soliton Solutions
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