Meshy soliton structures for (2+1)-dimensional integrable systems and interactions

TL;DR

This paper introduces new meshy soliton structures for (2+1)-dimensional integrable systems, providing explicit solutions and analyzing their interactions with lump structures, expanding understanding of complex soliton interactions.

Contribution

The paper constructs explicit meshy soliton solutions for specific (2+1)-dimensional integrable systems using Cole-Hopf transformations, revealing their linear or parabolic nature and interactions.

Findings

Explicit meshy soliton solutions derived

Interactions between meshy solitons and lumps analyzed

Solutions exhibit linear or parabolic structures

Abstract

In this letter, we construct new meshy soliton structures by using two concrete (2+1)-dimensional integrable systems. The explicit expressions based on corresponding Cole-Hopf type transformations are obtained. Constraint equation ft+\sum_{j=1}^{N} h_j(y)f_{jx} = 0 shows that these meshy soliton structures can be linear or parabolic. Interaction between meshy soliton structure and Lump structure are also revealed.