Mathematical methods via construction of traveling and solitary wave solutions of three coupled system of nonlinear partial differential equations and their applications

In this research work, we applying the modification form of extended auxiliary equation mapping method on three couple system of nonlinear ovulation equations which have odd and even partial derivatives. We investigated the new exact traveling and solitary wave solutions of coupled Whitham-Broer-Kaup, (2 + 1)-dimensional Broer-Kaup-Kupershmit and Drinfel’d-Sokolow-Wilson equations. We applied successfully this new method and obtained the new form of exact traveling and solitary wave solutions. As a results, obtained new solutions in the form of solitons, bright and dark solitons, kink and anti-kink type solitons, traveling wave, periodic solitary wave,trigonometric functions and elliptic functions solutions. These new different type of solutions are show the effectiveness and power of this new method and also show two and three dimensional graphically with the help of computer software Mathematica. These new solutions have many applications in the field of physics and other branches of applied science. We can also be solved other couple system of partial differential equations by this new technique. Keywords: Modified extended auxiliary equation mapping method, Whitham-Broer-Kaup equation, The (2 + 1)-dimensional Broer-Kaup-Kupershmit equation, Drinfel’d-Sokolow-Wilson equation, Solitary wave solutions, Exact traveling wave solution