Floquet's Theorem and Stability of Periodic Solitary Waves

被引：30

作者：

Neves, Aloisio ^{[1
]}

机构：

[1] Univ Estadual Campinas, Dept Matemat, IMECC, BR-13083970 Campinas, SP, Brazil

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2009年 / 21卷 / 03期

关键词：

Hill's operator; Spectrum; Periodic potential; Nonlinear stability;

D O I：

10.1007/s10884-009-9143-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the spectrum the Hill operator L(y) = -y '' + Q(x) y in L-per(2)[0, pi]. We show that the eigenvalues of L can be characterized by knowing one of its eigenfunctions. Applications are given to nonlinear stability of a class of periodic problems.

引用

页码：555 / 565

页数：11

共 11 条

[1]

AKHIEZER NI, 1990, MATH MONOGRAPHS, V79

[2]

ANGULO J, 2006, ADV DIFFERENTIAL EQU, V11, P1321

[3]

Byrd PF., 1954, Handbook of elliptic integrals for engineers and scientist

[4] Orbital stability of periodic waves for the nonlinear Schrodinger equation [J].

Gallay, Thierry ;

Haragus, Mariana .

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2007, 19 (04) :825-865

[5] STABILITY THEORY OF SOLITARY WAVES IN THE PRESENCE OF SYMMETRY .2. [J].

GRILLAKIS, M ;

SHATAH, J ;

STRAUSS, W .

JOURNAL OF FUNCTIONAL ANALYSIS, 1990, 94 (02) :308-348

[6] STABILITY THEORY OF SOLITARY WAVES IN THE PRESENCE OF SYMMETRY .1. [J].

GRILLAKIS, M ;

SHATAH, J ;

STRAUSS, W .

JOURNAL OF FUNCTIONAL ANALYSIS, 1987, 74 (01) :160-197

[7]

Haupt O, 1915, MATH ANN, V76, P67

[8]

Lopes O, 2002, DISCRETE CONT DYN S, V8, P115

[9]

MAGNUS W, 1966, INTERSIENCE TRACTS P, V20

[10] Isoinertial family of operators and convergence of KdV cnoidal waves to solitons [J].

Neves, Aloisio .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 244 (04) :875-886

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