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Solving the discrete KdV equation with homotopy analysis method. (English) Zbl 1209.65122
Summary: We apply the homotopy analysis method to differential-difference equations. We take the discrete KdV equation as an example, and successfully obtain double periodic wave solutions and solitary wave solutions. It illustrates the validity and the great potential of the homotopy analysis method in solving discrete KdV equation. Comparisons are made between the results of the proposed method and exact solutions. The results reveal that the proposed method is very effective and convenient.

MSC:
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35Q53 KdV equations (Korteweg-de Vries equations)
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