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Exact and numerical traveling wave solutions for nonlinear coupled equations using symbolic computation. (English) Zbl 1048.65096
Summary: We find the explicit and numerical traveling wave solutions for a coupled Korteweg-de Vries (KdV) equation and a coupled modified KdV (MKdV) equation by using the decomposition method with help of symbolic computation. By using this method, the solutions were calculated in the form of a convergent power series with easily computable components. The convergence of the method as applied to the coupled KdV and MKdV equations is illustrated numerically.

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
68W30 Symbolic computation and algebraic computation
Full Text: DOI
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