Searching Display Solutions Of The Classical Fisher Equation By Some Function Transformation Methods

Under guide of the soliton theory and the Lie group transformation, byusing some exact function transformation methods which are common used tolooking for solutions of nonlinear evolutionary di?erential equation(s) today, andcooperated computing software Mathematica, this paper gains some new displaysolutions of the classical Fisher equation.It is divided into three chapters. The first chapter is introduction of back-ground and direction of getting display solutions, including the soliton theory,the Lie group transformation, computer's assistance, types of display solutionsand methods of searching display solutions etc. The second chapter focuses onsome function transformation methods which were used in the writer's researchwork such as the homogeneous balance method, the generalized tanh-methodand its expand, the complex tanh-function expansion method, the generalizedpower-exponent function method etc, and some research results of Fisher-typeequation especially some display solutions of such type. The third chapter dealswith the commonest form of classical Fisher equationby using some exact function transformation methods such as the homogeneousbalance method, the generalized tanh-method and its expand, the complex tanh-function expansion method, the generalized power-exponent function methodand with modern mathematics computing software Mathematica to get somedesired display solutions of the equation.In the third chapter, firstly depending on some principles of the tanh-function method, we adopt a simplest form of the Riccati equation...