Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
1995-09-25
Nonlinear Sciences
Pattern Formation and Solitons
Minor corrections, new discussion added, version to appear in J. Phys. Soc. Japan
Scientific paper
We apply a multiple-time version of the reductive perturbation method to study long waves as governed by the shallow water wave model equation. As a consequence of the requirement of a secularity-free perturbation theory, we show that the well known N-soliton dynamics of the shallow water wave equation, in the particular case of $\alpha=2 \beta$, can be reduced to the N-soliton solution that satisfies simultaneously all equations of the Korteweg-de Vries hierarchy.
Kraenkel Roberto A.
Manna M. A.
Montero J. C.
Pereira J. G.
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