Extended Transformed Rational Function Method to Nonlinear Evolution Equations

In this work, we study complexiton solutions to a (2+1)-dimensional (SK) equation and a (3+1)-dimensional nonlinear evolution equation. The complexiton solutions are combinations of trigonometric function waves and exponential function waves. For this goal, the extended transformed rational function method is carried out which is based on the Hirota bilinear forms of the considered equations and provides a systematical and convenient tool for constructing the exact solutions of nonlinear evolution equations.

Application of Extended Transformed Rational Function Method to Some (3+1) Dimensional Nonlinear Evolution Equations

The transformed rational function method can be considered as unification of the tanh type methods, the homogeneous balance method, the mapping method, the exp-function method and the F-expansion type methods. In this paper, we present complexiton solutions of (3+1) dimensional Korteweg-de Vries (KdV) equation and a new (3+1) dimensional generalized Kadomtsev-Petviashvili equation by using extended transformed rational function method which provides very useful and effective way to obtain complexiton solutions of nonlinear evolution equations.

Exact solutions of the Rosenau–Hyman equation, coupled KdV system and Burgers–Huxley equation using modified transformed rational function method

In this research, we study the exact solutions of the Rosenau–Hyman equation, the coupled KdV system and the Burgers–Huxley equation using modified transformed rational function method. In this paper, the simplest equation is the Bernoulli equation. We are not only obtain the exact solutions of the aforementioned equations and system but also give some geometric descriptions of obtained solutions. All can be illustrated vividly by the given graphs.