Emad K. JARADAT, Amer D. ALOQALI, Wajd ALHABASHNEH The nonlinear Klein-Gordon equation used to model many nonlinear phenomena. In quantum field theory, the corresponding Klein-Gordon field characterized by “particles” with rest mass m and no other structure (e.g., no spin, no electric charge, etc.) Therefore, the Klein-Gordon field is physically the simplest of the relativistic fields that one can study. In this paper, an analytical technique proposed to solve the nonlinear Klein-Gordon equation with high order nonlinearity. The proposed method based on applying the Laplace transform to nonlinear partial differential equation and replacing the nonlinear terms by the Adomian polynomials. This method known as the Laplace decomposition method (LDM). The obtained approximate analytical solution of the equation will be in the form of a summation with easily obtainable terms. An application discussed to illustrate the effectiveness and the performance of the proposed method, which successively provided for finding the solutions of the nonlinear Klein-Gordon equation.
USING LAPLACE DECOMPOSITION METHOD TO SOLVE NONLINEAR KLEIN-GORDON EQUATION
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- Written by Emad K. JARADAT, Amer D. ALOQALI, Wajd ALHABASHNEH
- Category: Physics
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