Abstract
Among the most interesting things Russell discovered was there is a mathematical relation between the height of the wave, the depth of the wave when water at rest and the speed at which the wave travels. KdV equation was the first mathematical unidimensional model describing the phenomenon observed by Scott-Russell. Despite its nonlinearity and dispersivity terms, KdV equation has being interesting because of its integrability, and specially being a soliton equation. In this paper, we aim to analyze an extended KdV equation. The construction of approximate solution of this equation will be done in Hs(R), for s>52, using the modified energy method, its uniqueness and continuity with respect to the initial data is presented referring to a Bona–Smith technique.
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