Novel hyperbolic behaviors to some important models arising in quantum science

Abstract

In this study, with the help of Wolfram Mathematica 9 software, the powerful sine-Gordon expansion method is used in constructing new hyperbolic function solutions to the two well known nonlinear differential equations that arise in the field of nonlinear sciences, namely; the modified Zakharov-Kuznetsov and the (2+1)-dimensional cubic Klein-Gordon equations. We also plot the two-and three-dimensional graphics of all the obtained solutions in this paper by utilizing the same program in the Wolfram Mathematica 9 software.