Abstract
This article presents triple Laplace transform coupled with iterative method to obtain the exact solution of two-dimensional nonlinear sine-Gordon equation (NLSGE) subject to the appropriate initial and boundary conditions. The noise term in this equation is vanished by successive iterative method. The proposed technique has the advantage of producing exact solution, and it is easily applied to the given problems analytically. Four test problems from mathematical physics are taken to show the accuracy, convergence, and the efficiency of the proposed method. Furthermore, the results indicate that the introduced method is promising for solving other type systems of NLPDEs.
Highlights
The sine-Gordon (SG) equation is a nonlinear hyperbolic PDE, which was originally considered in the nineteenth century in the course of study of surfaces of constant negative curvature often used to describe and simulate the physical phenomena in a variety of fields of engineering and science, such as nonlinear waves, propagation of fluxons, and dislocation of metals [1,2,3,4]
Fayadh and Faraj [9] applied combined Laplace transform method and VIM to get the approximate solution of the one-dimensional sine-Gordon equation
Using triple Laplace transform coupled with new iterative method, we introduce the recursive relations and get u0ðx, y, tÞ = Lxyt−1
Summary
The sine-Gordon (SG) equation is a nonlinear hyperbolic PDE, which was originally considered in the nineteenth century in the course of study of surfaces of constant negative curvature often used to describe and simulate the physical phenomena in a variety of fields of engineering and science, such as nonlinear waves, propagation of fluxons, and dislocation of metals [1,2,3,4]. The purpose of this paper, is to apply triple Laplace transform (TLT) and iterative method (IM) developed in [38] to find the exact solution of two-dimensional nonlinear sine-Gordon equation (NLSGE) subject to appropriate initial and boundary conditions. Dhunde and Waghmare in [37, 39] applied double Laplace transform iteration method (TLTIM) to solve nonlinear Klein-Gordon and telegraph equations. By this method, the noise terms disappear in the iteration process, and single iteration gives the exact solution.
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