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 |
Keywords:
Adomian decomposition method; coupled KdV equation; traveling wave solution; symbolic computation; Korteweg-de Vries equation; convergence; numerical examplesReferences:
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