Abstract
In this article, an exact lump solution, snoidal wave solution and one topological soliton solution having a special feature, are obtained for the integrable (2+1) dimensional Kundu–Mukherjee–Naskar (KMN) equation. These solutions have an unusual property that they can get curved in the x–y 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 in the field of nonlinear optics. This novel feature, which is an unusual 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.
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