Whitham modulation theory for the Kadomtsev-Petviashvili equation

被引：29

作者：

Ablowitz, Mark J. ^{[1
]}

Biondini, Gino ^{[2
,3
]}

Wang, Qiao ^{[2
]}

机构：

[1] Univ Colorado, Dept Appl Math, Boulder, CO 80303 USA

[2] SUNY Buffalo, Dept Math, Buffalo, NY 14260 USA

[3] SUNY Buffalo, Dept Phys, Buffalo, NY 14260 USA

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2017年 / 473卷 / 2204期

基金：

美国国家科学基金会;

关键词：

Kadomtsev-Petviashvili equation; small dispersion limit; Whitham equations; dispersive shock waves; dispersive regularizations; water waves; DISPERSIVE SHOCK-WAVES; DE-VRIES EQUATION; CAUCHY-PROBLEM; SYSTEMS; INTEGRABILITY; STABILITY;

D O I：

10.1098/rspa.2016.0695

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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 Vriese quation 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.

引用

页数：23

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