New Hyperbolic Function Solutions for Some Nonlinear Partial Differential Equation Arising in Mathematical Physics

Abstract

In this study, we investigate some new analytical solutions to the (1 + 1)-dimensional nonlinear Dispersive Modified Benjamin–Bona–Mahony equation and the (2 + 1)-dimensional cubic Klein–Gordon equation by using the generalized Kudryashov method. After we submitted the general properties of the generalized Kudryashov method in Section 2, we applied this method to these problems to obtain some new analytical solutions, such as rational function solutions, exponential function solutions and hyperbolic function solutions in Section 3. Afterwards, we draw two- and three-dimensional surfaces of analytical solutions by using Wolfram Mathematica 9.

Keywords

• the generalized Kudryashov method
• (1 + 1)-dimensional nonlinear Dispersive Modified Benjamin–Bona–Mahony equation
• (2 + 1)-dimensional cubic Klein–Gordon equation
• soliton solutions
• rational function solutions
• hyperbolic function solutions
• trigonometric function solutions
• exponential function solution