Extracting traveling wave solutions for two nonlinear models of NPDEs in mathematical physics

Abstract In this work, we apply the Riccati-Bernoulli (RB) sub-ODE approach to provide some vital solitary wave solutions for the nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and the Klein-Gordan (KG) equation. The solutions that are provided here are helpful in describing several physical phenomena in inharmonic crystals, cold plasma, compressible fluids and quantum mechanics. The proposed approach is effective and easy, resulting in new generalised solitonic wave profiles. For suitable free parameter values, two-dimensional (2D) and three-dimensional (3D) graphs are depicted to show the shape of the obtained solutions. We also show the effect of the physical parameters on the behaviour of the solutions. Finally, the suggested approach may be extended to different equations appearing in mathematical physics.