Solitary Wave Solutions to (2+1)-Dimensional Coupled Riemann Wave Equations and Their Applications in Mathematical Physics

This paper employs the generalized projective Riccati equation method and the Sardar sub-equation technique to extract the solitary wave solutions of the nonlinear (2+1)-dimensional Coupled Riemann wave equations, which describes the electrostatic and magneto-sound waves in plasma, ion cyclotron waves, tidal and tsunami waves, homogeneous and stationary media etc. The obtained solitary wave solutions are represented as exponential, trigonometric, and hyperbolic functions. By setting certain values of the parameters, we acquire smooth kink and smooth anti-kink solitons, smooth bell shaped solitons, anti-bell shaped solitons, periodic shape solitons, peakon and anti-peakon solitons, and other solitons. Graphical representation in both 2D and 3D is provided by using mathematica to analyze dynamic behavior of waves. It is visualized that wave number and wave speed controls the behaviour of soliton. These methods are applied for the first time on the proposed equation and considered as most recent techniques to acquire soliton solutions for the proposed problem.