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On the Derivation of the Modified Kadomtsev‐Petviashvili Equation

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It is well known that the Kadomtsev‐Petviashvili (KP) equation is the two‐dimensional analogue of the Korteweg—de Vries (KdV) equation. We reconsider the derivation of the KP equation, modified to include the effects of rotation, in order to determine the nature of the initial conditions. The motivation for this is that if the solutions of the modified KP equation are assumed to be locally confined, then they satisfy a certain constraint, which appears to restrict considerably the class of allowed initial conditions. The outcome of the analysis presented here is that in general it is not permissible to assume that solutions of the modified KP equation are locally confined, and hence the constraint cannot be applied. The reason for this is the radiation of PoincarĂ© waves, which appear behind the main part of the solution described by the modified KP equation.
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Document Type: Research Article

Publication date: June 1, 1989

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