Probabilities and Probable Solutions of a Modified KdV Type Nonlinear Partial Differential Equation

Abstract

The goal of this work is not only the search for the solutions of a nonlinear partial differential equation, but how to locate and choose a form of solution verifying the nonlinear partial differential equation. In this work, we use the probabilities of appearance of the pairs (n, m) linked to iB-functions for which certain terms of the range of coefficients equations are grouped together to locate and then determine the solutions of the partial differential equation of the KdV type. The pairs (n, m) when identified, indicate with precision the iB-function which will choose from the start as the solution function which we want to build. The probabilities here are essential data to select the analytical sequences of the solutions to be investigated.

Abundant optical solutions for the Sasa-Satsuma equation with M-truncated derivative

“…Similarly, we can replace F (η δ ) in (32) with cn(Kη δ , m) or dn(Kη δ , m) to derive the solutions of Eq. 15 as follows:…”