Optical solitons and exact solutions of the (2+1) dimensional conformal time fractional Kundu-Mukherjee-Naskar equation via novel extended techniques

The current work uses a (2+1) dimensional conformal time fractional Kundu-Mukherjee-Naskar (KMN) model to investigate optical soliton transmission across an optical fiber that maintains polarization. Three constructive techniques, namely, the extended power series solution, the new generalized method, and the extended sinh-Gordon expansion method are utilized to find the exact soliton solutions of this model. The invariant analysis has been performed on the (2+1) dimensional time fractional KMN model by using the conformal time fractional derivative. The symmetries obtained using conformal fractional derivative are compared with the symmetries obtained for integer order KMN model because symmetries using Riemann Liouville fractional derivative turned out to be trivial. The given system of fractional PDEs has been reduced by using differential invariants obtained from various linear combinations of vector fields associated with the infinitesimal generator of symmetry transformations. These reduced systems of equations are then investigated for their exact solutions.