Exact soliton solution for systems of non-linear (2+1)D-DEs

In this article exact soliton solution for models as system of (2+1) dimensional PDEs will be obtain by using reliable manner depend on combined LA-transform with decomposition technique and the results has shown a high-precision, smooth and the series solution is converge rapidly to exact analytic solution compared with other classic approaches. Suggested approach not needs any discretization by data of domain or presents assumption or neglect for a perturbation parameter in problems and not need to use any assumption to convert the non-linear terms into linear. Two examples such as system of (2+1) D-Bogoyavlenskii’s breaking soliton equation and system of (2+1) D-Ito equation has been presented to show the convergence of solution obtained by suggested method to the exact.