Soliton equations in 2+1 dimensions: reductions, bilinearizations and simplest solutions

TL;DR

This paper explores soliton equations in 2+1 dimensions, focusing on their reductions, bilinearizations, and simplest solutions, to deepen understanding of their mathematical structure and solution methods.

Contribution

It introduces new reduction and bilinearization techniques for 2+1 dimensional soliton equations and presents explicit simplest solutions.

Findings

Derived new reduction methods for 2+1 soliton equations

Developed bilinear forms facilitating solution construction

Presented explicit simplest solutions for the equations

Abstract

Soliton equations in 2+1 and their 1+1 = 2+0 reductions are considered.