A Fresh Solitary Solutions for Coupled Maccari’s System Using by Extended Rational sine-cosineand Rational sinh-cosh Methods

Modeling natural phenomena with the equation system andtheir optimization is of special importance. One of theseequations is the coupled Maccaris system. The aim of thisstudy is to find new optimal exact solutions to the coupledMaccaris system by extended rational sine-cosine andrational sinh-cosh methods. By means of these methods, wefound some fresh solitons of the above mentioned equation.The solutions are expressed in the form of new periodic,dark, bright and bright periodic solitons solutions. Thesemethods are efficient, powerful, and they can be used as analternative to establish new soliton of different types ofdifferential PDEs applied in mathematical physics. Also, inorder to visualize the underlying dynamics of the obtainedsoliton solutions, ۲D and ۳D plots are drawn.Computational results indicate not only the efficiency andstrength of the methods but also further possibleapplicability potential of these techniques to some othersignificant nonlinear PDEs.