# Bilinear approach to the supersymmetric Gardner equation

## TL;DR

This paper introduces a new supersymmetric Gardner equation, constructs its soliton solutions, and explores rational solutions and dynamics, advancing understanding of supersymmetric integrable systems.

## Contribution

It presents the first supersymmetric Gardner equation, develops its superbilinear formalism, and derives explicit soliton and rational solutions.

## Key findings

- Constructed supersymmetric solitons.
- Derived rational nonsingular solutions.
- Analyzed solution dynamics in the supersymmetric context.

## 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.