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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.

MSC:
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
Software:
MACSYMA
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References:
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