Water-wave motion is a fascinating subject of fluid mechanics. Apart from being important in various branches of engineering and applied science, many water-wave phenomena are also familiar from everyday experience; obtaining a thorough understanding of the relevant physical mechanisms, however, presents fluid dynamicists with great challenges. Since the early work of Airy and Stokes in the middle of the previous century, it has been recognized that, even under the assumption of potential flow, the water-wave equations are analytically intractable in general. The main difficulty stems from the nonlinear boundary conditions that apply on the free surface, which itself is unknown and is to be determined as part of the solution. In recent years, considerable progress has been made in illuminating some aspects of water-wave propagation-most notably the interplay of weak finite-amplitude and dispersive effects-using approximate (model) equations, valid asymptotically in certain limits. Combined with experi mental observations, these asymptotic theories reveal useful insights into the relevant physics. Moreover, in many instances, they have provided the impetus for related computational efforts. Perhaps the most well known model equation for water waves, first proposed about a century ago [see Miles (1981) for a review including historical details], is the Korteweg-de Vries (KdV) equation (Korteweg & de Vries 1895):
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T. R. Akylas (1994) studied this question.