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Abstract
in thesis , the most numerical solution of the MKDV+ is studied by two approaches. The first approach is to use a conventional Galerkin method with trial functions taken as Wavelet functions with Debauchies scaling factor D6. The second approach, is introduced by applying a splitting technique to the MKDV+ equation which produces a two equation system. The produced system of equations is solved by using conventional Galerkin method with weight and trial functions taken as Wavelet functions with Debauchies scaling factor D6. A comparative study between the present two methods and earlier methods in the literature are presented whenever possible.