Infinitely many radial solutions of a variational problem related to dispersion-managed optical fibers

被引：9

作者：

Kunze, M ^{[1
]}

机构：

[1] Univ Essen Gesamthsch, Fachbereich Math 6, D-45117 Essen, Germany

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2003年 / 131卷 / 07期

关键词：

nonlocal variational problem; compactness by symmetry; infinitely many solutions; nonlinear optics; dispersion managed solitons;

D O I：

10.1090/S0002-9939-02-06780-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a non-local variational problem whose critical points are related to bound states in certain optical fibers. The functional is given by phi(u) = 1/2\u\(2)(H1) - integral(0)(1) integral(R2) \e(itDelta)u\(4) dxdt, and relying on the regularizing properties of the solution e(itDelta) to the free Schrodinger equation, it will be shown that phi has in finitely many critical points.

引用

页码：2181 / 2188

页数：8

共 17 条

[1]

BERESTYCKI H, 1983, ARCH RATION MECH AN, V82, P313

[2]

BERESTYCKI H, 1983, ARCH RATION MECH AN, V82, P347

[3]

BOURGAIN J, 1999, C PUBLICATIONS AM MA, V46

[4]

Cazenave T., 1996, INTRO NONLINEAR SCHR, V3rd

[5] 8X10 GB/S TRANSMISSION THROUGH 280-KM OF DISPERSION-MANAGED FIBER [J].

CHRAPLYVY, AR ;

GNAUCK, AH ;

TKACH, RW ;

DEROSIER, RM .

IEEE PHOTONICS TECHNOLOGY LETTERS, 1993, 5 (10) :1233-1235

[6] Breathing solitons in optical fiber links [J].

Gabitov, I ;

Turitsyn, SK .

JETP LETTERS, 1996, 63 (10) :861-866

[7] Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation [J].

Gabitov, IR ;

Turitsyn, SK .

OPTICS LETTERS, 1996, 21 (05) :327-329

[8]

JACKSON R, UNPUB CRITICAL POINT

[9] Bifurcation from the essential spectrum without sign condition on the nonlinearity [J].

Kunze, M .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2001, 131 :927-943

[10] PRINCIPLE OF SYMMETRIC CRITICALITY [J].

PALAIS, RS .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1979, 69 (01) :19-30

← 1 2 →