Constructing soliton solutions and super-bilinear form of lattice supersymmetric KdV equation

With the coupling of a scalar field, a generalization of the nonlinear Klein–Gordon equation which arises in the relativistic quantum mechanics and field theory, i.e., the coupled nonlinear Klein–Gordon equations, is investigated via the Hirota method. With the truncated Painlevé expansion at the constant level term with two singular manifolds, the coupled nonlinear Klein–Gordon equations are transformed to a bilinear form. Starting from the bilinear form, with symbolic computation, we obtain the N-soliton solutions for the coupled nonlinear Klein–Gordon equations.

Download Full-text

Soliton solutions to KdV equation with spatio-temporal dispersion

Ocean Engineering ◽

10.1016/j.oceaneng.2016.01.022 ◽

2016 ◽

Vol 114 ◽

pp. 192-203 ◽

Cited By ~ 20

Author(s):

Houria Triki ◽

Turgut Ak ◽

Seithuti Moshokoa ◽

Anjan Biswas

Keyword(s):

Kdv Equation ◽

Soliton Solutions ◽

Spatio Temporal ◽

Temporal Dispersion

Download Full-text

Bilinear Approach to Supersymmetric KdV Equation

Journal of Nonlinear Mathematical Physics ◽

10.2991/jnmp.2001.8.s.9 ◽

2001 ◽

Vol 8 (sup1) ◽

pp. 48-52 ◽

Cited By ~ 4

Author(s):

A S Carstea

Keyword(s):

Kdv Equation ◽

Supersymmetric Kdv Equation ◽

Bilinear Approach

Download Full-text

BI-HAMILTONIAN STRUCTURE OF THE SUPERSYMMETRIC NONLINEAR SCHRÖDINGER EQUATION

Modern Physics Letters A ◽

10.1142/s0217732395002179 ◽

1995 ◽

Vol 10 (27) ◽

pp. 2019-2028 ◽

Cited By ~ 2

Author(s):

J.C. BRUNELLI ◽

ASHOK DAS

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Hamiltonian Structure ◽

Kdv Equation ◽

Nonlinear Schrodinger Equation ◽

Hamiltonian Reduction ◽

Hamiltonian Structures ◽

Nonlinear Schrödinger ◽

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.

Download Full-text

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.

Download Full-text