The Role of the Korteweg–de Vries Hierarchy in the N–Soliton Dynamics of the Shallow Water Wave Equation
نویسندگان
چکیده
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 α = 2β, can be reduced to the N–soliton solution that satisfies simultaneously all equations of the Korteweg–de Vries hierarchy.
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