Whitham modulation theory for the Kadomtsev-Petviashvili equation

2016/10/31 by Mark J. Ablowitz, Gino Biondini, Qiao Wang · 3 citations
Physics and Astronomy · #nlin.PS #nlin.SI

paper · pdf · doi:10.1098/rspa.2016.0695

published as Roy. Soc. Proc. A Vol. 473, p. 20160695 (2017) · Significantly revised version

arxiv created 2017/08/09 · arxiv updated 2017/08/10

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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• Modulation theory for lumps and interactions between lumps and a mean field in the Kadomtsev-Petviashvili equation

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