On The Existence Conditions for New Kinds of Solutions to (3+1)-Dimensional mKDV and mBBM Equations

Abstract

In this work, we consider (3+1) dimensional nonlinear partial differential equations, namely modified KdV and Benjamin-Bona-Mahony equations. Different types of solutions to these equations are derived by Jacobi elliptic sine function expansion method. Besides that, we introduce new types of solutions for two more modified forms of given equations. The gained solutions include exact, singular, periodic, and kink solutions. It is stated that some conditions related to the coefficients provide us with the existence of the gained solutions.