Soliton solutions for the N=2 supersymmetric KdV equation

We show that the supersymmetric nonlinear Schrödinger equation is a bi-Hamiltonian integrable system. We obtain the two Hamiltonian structures of the theory from the ones of the supersymmetric two-boson hierarchy through a field redefinition. We also show how the two Hamiltonian structures of the supersymmetric KdV equation can also be derived from a Hamiltonian reduction of the supersymmetric two-boson hierarchy.

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Nonholonomic deformation of coupled and supersymmetric KdV equations and Euler–Poincaré–Suslov method

Reviews in Mathematical Physics ◽

10.1142/s0129055x15500117 ◽

2015 ◽

Vol 27 (04) ◽

pp. 1550011 ◽

Cited By ~ 4

Author(s):

Partha Guha

Keyword(s):

Kdv Equation ◽

Infinite Dimensional ◽

Kdv Equations ◽

Finite Dimensional ◽

Euler Top ◽

Two Component ◽

Finite Dimensional Case ◽

Coupled Kdv Equations ◽

The Right ◽

Supersymmetric Kdv Equation

Recently, Kupershmidt [38] presented a Lie algebraic derivation of a new sixth-order wave equation, which was proposed by Karasu-Kalkani et al. [31]. In this paper, we demonstrate that Kupershmidt's method can be interpreted as an infinite-dimensional analogue of the Euler–Poincaré–Suslov (EPS) formulation. In a finite-dimensional case, we modify Kupershmidt's deformation of the Euler top equation to obtain the standard EPS construction on SO(3). We extend Kupershmidt's infinite-dimensional construction to construct a nonholonomic deformation of a wide class of coupled KdV equations, where all these equations follow from the Euler–Poincaré–Suslov flows of the right invariant L2 metric on the semidirect product group [Formula: see text], where Diff (S1) is the group of orientation preserving diffeomorphisms on a circle. We generalize our construction to the two-component Camassa–Holm equation. We also give a derivation of a nonholonomic deformation of the N = 1 supersymmetric KdV equation, dubbed as sKdV6 equation and this method can be interpreted as an infinite-dimensional supersymmetric analogue of the Euler–Poincaré–Suslov (EPS) method.

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New Dark Soliton Solutions of the KdV Equation

Communications in Theoretical Physics ◽

10.1088/0253-6102/20/4/493 ◽

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

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A new integrable equation combining the modified KdV equation with the negative-order modified KdV equation: multiple soliton solutions and a variety of solitonic solutions

Waves in Random and Complex Media ◽

10.1080/17455030.2017.1367440 ◽

2017 ◽

Vol 28 (3) ◽

pp. 533-543 ◽

Cited By ~ 12

Author(s):

Abdul-Majid Wazwaz

Keyword(s):

Kdv Equation ◽

Soliton Solutions ◽

Integrable Equation ◽

Multiple Soliton Solutions ◽

Negative Order ◽

Modified Kdv Equation

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

Modern Physics Letters B ◽

10.1142/s0217984909019934 ◽

2009 ◽

Vol 23 (14) ◽

pp. 1771-1780 ◽

Cited By ~ 3

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.

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