Novel curved solitons of integrable (2 +1) dimensional KMN equation

TL;DR

This paper derives exact lump and topological soliton solutions of the integrable (2+1)D KMN equation, revealing their ability to bend arbitrarily in the plane, which is useful for modeling physical wave phenomena.

Contribution

It introduces a novel class of curved soliton solutions in an integrable (2+1)D equation, enabled by Galilean covariance and current-like nonlinearity.

Findings

Solutions can bend arbitrarily in the plane.

The solutions are applicable to modeling physical wave structures.

The solutions are derived analytically for the first time.

Abstract

In this letter, the unique exact lump and topological soliton solutions of integrable (2+1) dimensional Kundu Mukherjee Naskar (KMN) equation are obtained. These solutions have an unusual property that they can get curved in the plane arbitrarily due to the presence of an arbitrary function of space(x) and time(t) in their analytic forms. Due to this special feature, the solutions can be used to model the bending of optical solitonic beam, different types of wave structures in real physical experimental conditions. This novel feature, which is a rare property for a constant coefficient completely integrable equation, arises due to the Galilean co-variance property and current like nonlinearity present in the KMN equation.