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

Abstract

Hirota bilinear form and multisoliton solution for semidiscrete and fully discrete (difference-difference) versions of supersymmetric KdV equation found by Xue, Levi and Liu [1] is presented. The solitonic interaction term displays a fermionic dressing factor as in the continuous supersymmetric case. Using bilinear equations it is shown also that there can be constructed a new integrable semidiscrete (and fully discrete) version of supersymmetric KdV which has simpler bilinear form but more complicated interaction dressing. Its continuum limit is also computed.

Supersymmetric Sawada-Kotera Equation: Bäcklund-Darboux Transformations and Applications

“…Bäcklund transformations have been known to be an effective approach to construction of solutions for nonlinear systems, furthermore they may be applied to generate new integrable systems, both continuous and discrete [26,27,18]. It is remarked that the applications of Bäcklund transformations to integrable discretization of super or supersymmetric integrable systems were developed only recently [16,48,45,46,47,4,31].…”

An algebraically stable variety for a four-dimensional dynamical system reduced from the lattice super-KdV equation

“…In a prior paper [6], applying the traveling wave reduction to the lattice super-KdV equation [3,18] in a case of finitely generated Grassmann algebra, the authors obtained a fourdimensional discrete integrable dynamical system ϕ :…”

Super-QRT and 4D-mappings reduced from the lattice super-KdV equation

“…It is a coupled system of nonlinear discrete equations having two dependent variables with values in the commutative (bosonic) and anti-commutative (fermionic) sector of an infinite dimensional Grassmann algebra. The motivation comes from the recent construction of lattice super-KdV equation [17], where the Lax pair, consistency around the cube and super-multisoliton solution were constructed [1]. In this paper we consider the traveling wave reduction of the lattice super-KdV which gives an example of a super-QRT mapping as a fourth order mapping.…”