Whitham modulation theory for the Kadomtsev– Petviashvili equation-Reference-Cited by-同舟云学术

Whitham modulation theory for the Kadomtsev– Petviashvili equation

Published:2017-08 Issue:2204 Volume:473 Page:20160695
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Ablowitz Mark J.¹,Biondini Gino²³^ORCID,Wang Qiao²

Affiliation:

1. Department of Applied Mathematics, University of Colorado, Boulder, CO 80303, USA

2. Department of Mathematics, State University of New York, Buffalo, NY 14260, USA

3. Department of Physics, State University of New York, Buffalo, NY 14260, USA

Abstract

The genus-1 Kadomtsev–Petviashvili (KP)-Whitham system is derived for both variants of the 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–de Vries 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.

Funder

Division of Mathematical Sciences

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2016.0695

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