Abstract:
This thesis deals with finding exact analytical solution of two-dimensional nonlinear coupled Sine
Gordon equation subjected to initial and boundary conditions using triple Sumudu transform with
iterative method. It is aimed to obtain exact solution for two-dimensional nonlinear coupled Sine
Gordon equation. Description of this analytical iterative methods and their convergence properties
has been presented. Exact solution were obtained using the convergence series form and presented
in the form of graphs. The solution of the nonlinear part of the coupled equations was solved a
successive iterative method. The applied methods are powerful and efficient for solving the problem
under consideration. The efficiency of the proposed methods was demonstrated by solving two
different test problems. Illustrative examples were taken from Mathematical Physics problems to
demonstrate the applicability and efficiency of the method. Finally we came to the conclusion that
the proposed method are very promising, efficient and powerful than other methods in terms of
providing exact solutions
