Exact solutions for the generalized nonlinear heat conduction equations using the exp-function method

New Explicit Exact Solutions of Nonlinear Evolution Equations Using the Generalized Auxiliary Equation Method Combined with Exp-function Method

Abstract:In this paper, we utilize the Exp-function method with symbolic computational system Maple to constructing generalized solitary solutions of auxiliary equation. With the aid of auxiliary equation and its generalized solitary solutions, new exact solutions with three arbitrary functions of two nonlinear evolution equations in physics, namely, higher-order nonlinear Schrodinger equation ...

Solutions of Nonlinear Differential Equations by Exp-function Method

Abstract: In this paper, we apply the exp-function method to construct solutions of nonlinear differential equations which arise in various branches of physics, engineering and applied sciences. The proposed scheme proves to be very efficient and compatible to deal with the nonlinearity and versatility of the problems. Numerical results clearly indicate the reliability and efficiency of the sug...

The Extended Hyperbolic Function Method for Generalized Forms of Nonlinear Heat Conduction and Huxley Equations

The Exp-Function Method for the Riccati Equation and Exact Solutions of Dispersive Long Wave Equations

In this paper, the Exp-function method is used to seek new generalized solitonary solutions of the Riccati equation. Based on the Riccati equation and one of its generalized solitonary solutions, new exact solutions with three arbitrary functions of the (2+1)-dimensional dispersive long wave equations are obtained. Compared with the tanh-function method and its extensions, the proposed method i...

New exact solutions for the Kawahara equation using Exp-function method

Exact solutions of the Kawahara equation by Assas [L.M.B. Assas, J. Com. Appl. Math. 233 (2009) 97–102] are analyzed. It is shown that all solutions do not satisfy the Kawahara equation and consequently all nontrivial solutions by Assas are wrong. Recently Assas in [1] looked for exact solutions of the Kawahara equation using the Exp function method. This equation can be written as ut + α uux +...