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

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.