On soliton structure of higher order (2+1)-dimensional equations of a relaxing medium beneath high-frequency perturbations

TL;DR

This paper explores the soliton structures of new (2+1)-dimensional nonlinear PDEs modeling relaxing media under high-frequency perturbations, revealing various soliton patterns including loop, cusp, and hump shapes.

Contribution

It introduces novel (2+1)-dimensional NLPDEs for relaxing media and derives specific soliton solutions with distinct pattern formations.

Findings

Identified soliton solutions with loop, cusp, and hump shapes.

Demonstrated the existence of complex soliton patterns in the new equations.

Provided insights into wave behaviors in relaxing media under high-frequency effects.

Abstract

We investigate the soliton structure of novel (2+1)-dimensional nonlinear partial differential evolution(NLPDE) equations which may govern the behavior of a barothropic relaxing medium beneath high-frequency perturbations. As a result, we may derive some soliton solutions amongst which three typical pattern formations with loop-, cusp- and hump-like shapes.