Abstract
A relatively new decomposition method is presented to find the explicit and numerical solutions of the Korteweg–de Vries equation (KdV for short), Burgers' equation and Korteweg–de Vries Burgers' equation (KdVB for short) for the initial conditions. In this method, the solution is constructed in the form of a convergent power series with easily computable components. The computed results show that this method can be readily implemented to this type of nonlinear equations and good accuracy can be also achieved. Furthermore, this method does not require any transformations, linearization or weak nonlinearity assumptions for finding the explicit solution and any discretization technique for computing the numerical solution.
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