In this article, some exact, atypical, topological soliton solutions of the integrable Kundu–Mukherjee–Naskar (KMN) equation have been derived. Those soliton solutions can have atypical shapes like U shaped soliton, W shaped soliton, three hump soliton, periodic soliton etc. on the \(x-y\) plane. This property is quite unusual for integrable systems, because solitons usually travel along a line with constant amplitude and velocity. The property of curvature of the solitons on \(x-y\) plane occur due to the presence of an arbitrary nonlinear function in the argument of the solution. Such arbitrary function in the soliton solution can exist because of the current like nonlinearity and Galilean covariance present in the KMN equation. These solutions are quite uncommon in the field of integrable systems; that may be used for better mathematical modelling of physical systems enriching the field of nonlinear optics.
