Analytical Solution of Phi-Four Equation

We know that partial differential equations arising in various engineering applications, that semi-analytical solution of these equations is very important. The PHI-four equation is considered as a particular form of the Klein-Gordon equation. Thephi-four’s equation is very widely studied in different areas of Physics: Plasma Physics, Fluid Dynamics Quantum Field Theory, Solid State Physics and others. The objective and goal of this paper is to present the semi-analytical Solution of phi-four’s equation, one of the newest, powerfuland easy-to-use analytical methods is the homotopy perturbation method (HPM), which isapplied in this paper to solve phi-four’sequation with high nonlinearity order. Then, we solve phi-four’s equation with the homotopy analysismethod (HAM) and Adomian’s decomposition method (ADM) and obtain analytical solution. In the end, we compared the results of these three methods in solving phi-four’s equation with each other.The homotopy analysis method (HAM)contains the auxiliary parameter ? that provides us to adjust and control the convergence region of solution Series. .The study has highlighted the efficiency and capability of aforementioned methods in solving phi-four’s equation which has risen from a number of important physical phenomenon’s. The results can be used in similar works by researchers.