Abstract
The Karpman-Kaup equation is a generic limit model for one-dimensional long-wave short-wave resonant interaction within the Benney criterion. We show that (1) the input short-wave fields generate solitons, (2) the boundary inputs allow one to drive the soliton, (3) the spectral transform tool can be adapted to solve (linearize) the finite-interval problem and (4) the explicit solution provided by the semi-infinite interval limit produces a very accurate description of the finite-interval case. The argumentation is based on the solution of this equation by the inverse spectral transform and the results are obtained by numerical simulation of both the original system and its spectral transform. The main issue is the demonstration that the spectral transform is a quite practical and efficient tool and that it has in this case a simple and explicit expression in terms of the input and output short-wave field values.
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