Solutions of the (2+1)-dimensional KP, SK and KK equations generated by gauge transformations from non-zero seeds

TL;DR

This paper uses gauge transformations to generate new solutions for (2+1)-dimensional KP, SK, and KK equations from non-zero seeds, revealing differences in soliton solutions compared to zero seed cases.

Contribution

It introduces a method to derive new solutions from non-zero seeds for these equations and establishes a Galilean transformation relating them to known solutions.

Findings

Explicit single-soliton solutions are provided.

Differences in peak height and location are demonstrated.

Solutions are visualized in three figures.

Abstract

By using gauge transformations, we manage to obtain new solutions of (2+1)-dimensional Kadomtsev-Petviashvili(KP), Kaup-Kuperschmidt(KK) and Sawada-Kotera(SK) equations from non-zero seeds. For each of the preceding equations, a Galilean type transformation between these solutions $u_2$ and the previously known solutions $u_2^{\prime}$ generated from zero seed is given. We present several explicit formulas of the single-soliton solutions for $u_2$ and $u_2^{\prime}$, and further point out the two main differences of them under the same value of parameters, i.e., height and location of peak line, which are demonstrated visibly in three figures.