The extended generalized Riccati equation mapping method for the (1+1)-dimensional modified KdV equation

Abstract

In this article, the generalized Riccati equation mapping is extended by the (G-/G)-expansion method. 2 In this method, the auxiliary equation G'- = r + pG + qG2 is used and called the generalized Riccati equation, where p,q and r are arbitrary constants. We construct twenty five exact traveling wave solutions of the (1+1)-dimensional modified KdV equation involving parameter by applying this method. The solutions are presented in terms of the hyperbolic, the trigonometric and the rational functional form including solitons and periodic solutions. Moreover, it is worth mentioning that one of our obtained solutions is in good agreement with the existing results which in turn validates our other solutions. In addition, some of newly obtained solutions are described in the figures.