Some novel exponential function structures to the Cahn–Allen equation

Abstract

In this manuscript, we consider the Bernoulli sub-equation function method for obtaining new exponential prototype structures to the Cahn–Allen mathematical model. We obtained new results using this technique. We plotted two- and three-dimensional surfaces of the results using Wolfram Mathematica 9. At the end of this manuscript, we submitted a conclusion in a comprehensive manner.

Keywords:

• Cahn–Allen equation
• Bernoulli sub-equation function method
• exponential function solution
• rational function solution

Publıc Interest Statement

Finding new travelling wave solutions to the nonlinear partial differential equations, especially, some important mathematical models have been significant for public statement. For example, the mathematical models such as AIDS, HIV, AEROCPACE and OPTICAL STRUCTURES attract attention from all over the world. Obtaining new travelling wave solutions to such models give new ideas to scientists and experts. Finding new types of solutions require a knowledge about the properties of new methods because they give us new properties of mathematical models. This paper is devoted to the mathematical investigation of the Cahn–Allen equation in terms of new travelling wave solutions using Bernoulli sub-equation function method.

Additional information

Funding

Funding. The authors received no direct funding for this research.

Notes on contributors

Hasan Bulut

Hasan Bulut, PhD, is currently an associate professor of Mathematics in Firat University, Elazig, Turkey. He has published more than 100 articles in various journals. His research interests include stochastic differential equations, fluid and heat mechanics, finite element method, analytical methods for nonlinear differential equations, mathematical physics and computer programming.

Sibel Sehriban Atas

Sibel Sehriban Atas is a master’s student under the suprvision of Hasan Bulut. Her research interests include analytical methods such as Bernoulli sub-ODE method, and improved version of it for the nonlinear partial differential equations with integer order.

Haci Mehmet Baskonus

Haci Mehmet Baskonus, PhD, is currently an assistant professor of computer Engineering in Munzur University, Tunceli, Turkey. He has published more than 50 articles in various journals. His research interests include analytical and numerical methods such as sumudu transform method, homotopy perturbation method, improved Bernoulli sub-ODE method and modified exponential function method for the nonlinear partial differential equations with integer order and fractional order.