Pseudo-linear superposition principle based on generated pseudo-operations: applications

The superposition principle is a useful tool for constructing new solutions of ordinary and partial differential equations. Therefore, through this paper, we are considering the pseudo-linear superposition principle based on generated pseudo-operations of the following form: x oplus y = g^-1 (g(x) + g(y)) , x odot y = g^-1 (g(x)g(y)) , where g is a continuous generating function. Some possibilities of the pseudo-linear superposition principle are illustrated through its application on three different nonlinear partial differential equations.