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arXiv · 1610.03478

Whitham modulation theory for the Kadomtsev-Petviashvili equation

Mark J. Ablowitz·Gino Biondini·Qiao Wang
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Abstract

The genus-1 KP-Whitham system is derived for both variants of the Kadomtsev-Petviashvili (KP) equation (namely, the KPI and KPII equations). The basic properties of the KP-Whitham system, including symmetries, exact reductions, and its possible complete integrability, together with the appropriate generalization of the one-dimensional Riemann problem for the Korteweg-deVries equation are discussed. Finally, the KP-Whitham system is used to study the linear stability properties of the genus-1 solutions of the KPI and KPII equations; it is shown that all genus-1 solutions of KPI are linearly unstable while all genus-1 solutions of KPII {are linearly stable within the context of Whitham theory.

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Mark J. Ablowitz, Gino Biondini, Qiao Wang. 2017-08-09. Whitham modulation theory for the Kadomtsev-Petviashvili equation. https://doi.org/10.1098/rspa.2016.0695

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