Investigations of the exact and numerical solutions of some nonlinear partial differential equations

This study investigates a search for analytical solutions, exact and numerical approximations to distinct nonlinear models in distinct nonlinear science areas. The symbolic methods used to explore this search are the sine-Gordon expansion technique, the extended sinh-Gordon expansion technique, and the finite forward difference process for the exact and numerical approximations. In addition, the extended technique of sinh-Gordon expansion is simplified in order to obtain multiple solitary wave solutions. The nonlinear models we address in this work are; the Korteweg-de Vries (KdV) equation with dual-power law nonlinearity, the coupled nonlinear Maccari's system, the (2+1)-dimensional Zakharov-Kuznetsov modified equal width equation, the resonant nonlinear Schro ̈dinger equation with both Spatio-temporal and inter-modal dispersions, the conformable space-time fractional second-order nonlinear Schro ̈dinger equation, the decoupled nonlinear Schro ̈dinger equation arising in dual-core optical fibers, the long-short-wave interaction system, the (2+1)-dimensional nonlinear Chiral Schrodinger's equation, Benjamin-Bona-Mahony equation, and the coupled Boussinesq equation. Various kind of solitary wave solutions is presented. The reported results were compared with the previous results. On the other hand, the numerical and exact approximations to some of the studied models are presented.