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In this research work, fast and slow waves in exact solution of the Fisher/KPP-type equation are presented. The exact solution of the equation is also obtained and presented. So, the study can present capability of the technique in obtaining the exact solution of the equation.
The Laplace Adomian decomposition method (LADM) is used to solve the NewellWhitehead-Segel equation. As a result, exact solution of the equation is obtained.
In this paper, the KdV system and Burgers–Huxley Equation is studied by using numerical analysis. So, capability of the method in solving the nonlinear problems can be proved.
The Fitzhugh–Nagumo Equation is studied in order to determine dynamical behavior of the equation. The research work can be used in mathematical modeling of different phenomena in order to be analyzed and solved. So, more scientific achievements can be obtained.
The study is presented to analyze nonlinear dynamics of dissipative wave patterns for Newell-Whitehead-Segel equation. Thus, different models of wave patterns in the approximate as well as exact solutions of the equation is obtained and presented. The study can introduce a new method in type of solutions in Nonlinear Differential Equations.
In the study, the painleve analysis and backlund transformation methods are used to obtain the exact solution of the Burgers-Huxley Equation. As a result, the study presents capabilities of the methods in solving the nonlinear differential equations.