Abstract
In this article exact solution for nonlinear wave-like equations with variable coefficients will be obtain by using reliable manner depend on combined Laplace 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 of strongly nonlinear 2-dimensional space high order have been presented to show the convergence of solution obtained by suggested method to the exact.
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