Explicit quasi-periodic wave solutions and asymptotic analysis to the supersymmetric Ito's equation

TL;DR

This paper develops explicit quasi-periodic wave solutions for the supersymmetric Ito's equation using Riemann theta functions and bilinear forms, linking these solutions to solitons and analyzing their asymptotic behavior.

Contribution

It introduces a novel formula for constructing quasi-periodic solutions of the supersymmetric Ito's equation in superspace.

Findings

Quasi-periodic solutions are explicitly constructed from the formula.

Relations between periodic and soliton solutions are rigorously established.

Quasi-periodic solutions tend to soliton solutions under small amplitude limits.

Abstract

Based on a Riemann theta function and the super-Hirota bilinear form, we propose a key formula for explicitly constructing quasi-periodic wave solutions of the supersymmetric Ito's equation in superspace $\mathbb{C}_{\Lambda}^{2,1}$. Once a nonlinear equation is written in bilinear forms, then the quasi-periodic wave solutions can be directly obtained from our formula. The relations between the periodic wave solutions and the well-known soliton solutions are rigorously established. It is shown that the quasi-periodic wave solutions tends to the soliton solutions under small amplitude limits.