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Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method. (English) Zbl 1022.35051
Summary: We present a reliable algorithm to study the known model of nonlinear dispersive waves proposed by Boussinesq. The modified algorithm of the Adomian decomposition method is used with an emphasis on the single soliton solution. New exact periodic solutions and polynomial solutions are obtained. The results of numerical examples are presented and only few terms are required to obtain accurate solutions.

MSC:
35Q35 PDEs in connection with fluid mechanics
76B25 Solitary waves for incompressible inviscid fluids
35Q51 Soliton equations
35B10 Periodic solutions to PDEs
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