NONLINEAR-WAVE AND SCHRODINGER-EQUATIONS .1. INSTABILITY OF PERIODIC AND QUASI-PERIODIC SOLUTIONS

被引：70

作者：

SIGAL, IM ^{[1
]}

机构：

[1] PRINCETON UNIV,PRINCETON,NJ 08544

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 1993年 / 153卷 / 02期

关键词：

D O I：

10.1007/BF02096645

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We investigate stability of periodic and quasiperiodic solutions of linear wave and Schrodinger equations under non-linear perturbations. We show in the case of the wave equations that such solutions are unstable for generic perturbations. For the Schrodinger equations periodic solutions are stable while the quasiperiodic ones are not. We extend these results to periodic solutions of non-linear equations.

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页码：297 / 320

页数：24

相关论文

共 15 条

[1] PERTURBATION OF EMBEDDED EIGENVALUES IN THE GENERALIZED N-BODY PROBLEM [J].

AGMON, S ;

HERBST, I ;

SKIBSTED, E .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1989, 122 (03) :411-438

[2] PERIODIC-SOLUTIONS OF SOME INFINITE-DIMENSIONAL HAMILTONIAN-SYSTEMS ASSOCIATED WITH NON-LINEAR PARTIAL DIFFERENCE-EQUATIONS .1. [J].

ALBANESE, C ;

FROHLICH, J .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1988, 116 (03) :475-502

[3]

[Anonymous], 1987, SCHRODINGER OPERATOR

[4] EXPONENTIAL BOUNDS AND ABSENCE OF POSITIVE EIGENVALUES FOR N-BODY SCHRODINGER-OPERATORS [J].

FROESE, R ;

HERBST, I .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1982, 87 (03) :429-447

[5] SPECTRAL-ANALYSIS OF 2ND-ORDER ELLIPTIC-OPERATORS ON NONCOMPACT MANIFOLDS [J].

FROESE, R ;

HISLOP, P .

DUKE MATHEMATICAL JOURNAL, 1989, 58 (01) :103-129

[6] A NEW PROOF OF THE MOURRE ESTIMATE [J].

FROESE, R ;

HERBST, I .

DUKE MATHEMATICAL JOURNAL, 1982, 49 (04) :1075-1085

[7]

FROESE R, 1987, LECTURES SCATTERING

[8]

HORWITZ LP, 1979, HELV PHYS ACTA, V51, P685

[9] PERTURBATION OF EMBEDDED EIGENVALUES [J].

HOWLAND, JS .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 78 (02) :280-&

[10]

Kato T., 1966, PERTURBATION THEORY