Application of Bernoulli sub-equation function method to nonlinear differential equation

SUMMARY APPLICATION OF BERNOULLI SUB-EQUATION FUNCTION METHOD TO NONLINEAR DIFFERENTIAL EQUATION This thesis is composed of five chapter. In the first chapter, we investigate the literature in a general case. In second chapter, some important and fundamental definition and theorems are given. In third chapter, general properties of Bernoulli sub-equation function method are presented. In forth chapter, some new analytical solutions of the nonlinear evolution describing the Dynamics of ionic currents along Microtubules and we consider the Improved Bernoulli sub-equation function method for obtaining Coupled Konno-Oono Equation and Modified Boussinesq Equation. We obtain new results by using this techniques. Two- and three-dimensional surfaces of solution, are obtained by using Wolfram Mathematica 9. In the last section of this thesis, a comprehensive conclusion under the examples of finding are introduced. Key Words: Bernoulli Sub-Equation Function Method, Improved Bernoulli Sub-Equation Function Method, Coupled Konno-Oono Equation and Modified Boussinesq Equation.