Bilinear approach to the supersymmetric Gardner equation

Abstract

We study a supersymmetric version of the Gardner equation (both focusing and defocusing) using the superbilinear formalism. This equation is new and cannot be obtained from supersymmetric modified Korteweg-de Vries equation with a nonzero boundary condition. We construct supersymmetric solitons and then by passing to the long-wave limit in the focusing case obtain rational nonsingular solutions. We also discuss the supersymmetric version of the defocusing equation and the dynamics of its solutions.

arXiv comment13 pages

References in corpus (4)

• Supersymmetric Modified Korteweg-de Vries Equation: Bilinear Approach
• Supersymmetric Two-Boson Equation: Bilinearization and Solutions
• Bilinear Approach to N=2 Supersymmetric KdV equations
• Localised and nonlocalised structures in nonlinear lattices with fermions