Higher-order resonances and instability of high-frequency WKB solutions

被引：5

作者：

Lu, Yong ^{[1
]}

机构：

[1] Charles Univ Prague, Fac Math & Phys, Math Inst, Sokolovska 83, Prague 18675, Czech Republic

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 260卷 / 03期

关键词：

Higher-order resonances; WKB solutions; Transparency conditions; Instabilities; KLEIN-GORDON EQUATIONS; GLOBAL EXISTENCE;

D O I：

10.1016/j.jde.2015.10.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper focuses on the destabilizing role of resonances in high-frequency WKB solutions. Specifically, we study higher-order resonances associated with higher-order harmonics generated by nonlinearities. We give examples of systems and solutions for which such resonances generate instantaneous instabilities, even though the equations linearized around the leading WKB terms are initially stable, meaning in particular that the key destabilizing terms are not present in the data. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：2296 / 2353

页数：58

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