Hamiltonian flows for a reduced Maxwell-Bloch system with permanent dipole

被引：5

作者：

Agrotis, M ^{[1
]}

机构：

[1] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2003年 / 183卷 / 1-2期

基金：

美国国家科学基金会;

关键词：

reduced Maxwell-Bloch equations; Lie algebras; commuting flows; conservation laws;

D O I：

10.1016/S0167-2789(03)00158-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We place a reduced Maxwell-Bloch (rMB) system with permanent dipole in a Lie algebraic framework that enables us to reveal a hierarchy of systems in involution, the first of which is the rMB model. This is done in the context of the Adler-Kostant-Symes theorem. We provide the Hamiltonian functions for the commuting flows and establish an infinite number of conservation laws. (C) 2003 Elsevier B.V. All rights reserved.

引用

页码：141 / 158

页数：18

共 16 条

[1]

ABLOWITZ MJ, 1974, STUD APPL MATH, V53, P249

[2] COHERENT PULSE-PROPAGATION, A DISPERSIVE, IRREVERSIBLE PHENOMENON [J].

ABLOWITZ, MJ ;

KAUP, DJ ;

NEWELL, AC .

JOURNAL OF MATHEMATICAL PHYSICS, 1974, 15 (11) :1852-1858

[3]

ADLER M, 1979, INVENT MATH, V50, P219

[4] COMPLETELY INTEGRABLE SYSTEMS, EUCLIDEAN LIE-ALGEBRAS, AND CURVES [J].

ADLER, M ;

VANMOERBEKE, P .

ADVANCES IN MATHEMATICS, 1980, 38 (03) :267-317

[5] Complete integrability of the reduced Maxwell-Bloch equations with permanent dipole [J].

Agrotis, M ;

Ercolani, NM ;

Glasgow, SA ;

Moloney, JV .

PHYSICA D, 2000, 138 (1-2) :134-162

[6] SOLITONS IN NONLINEAR OPTICS .1. MORE ACCURATE DESCRIPTION OF 2PI PULSE IN SELF-INDUCED TRANSPARENCY [J].

EILBECK, JC ;

GIBBON, JD ;

CAUDREY, PJ ;

BULLOUGH, RK .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1973, 6 (09) :1337-1347

[7]

Faddeev L. D., 1987, HAMILTONIAN METHODS

[8] TODA LATTICE .2. EXISTENCE OF INTEGRALS [J].

FLASCHKA, H .

PHYSICAL REVIEW B, 1974, 9 (04) :1924-1925

[9] KAC-MOODY LIE-ALGEBRAS AND SOLITON-EQUATIONS .2. LAX EQUATIONS ASSOCIATED WITH A1 [J].

FLASCHKA, H ;

NEWELL, AC ;

RATIU, T .

PHYSICA D, 1983, 9 (03) :300-323

[10] KAC-MOODY LIE-ALGEBRAS AND SOLITON-EQUATIONS .3. STATIONARY EQUATIONS ASSOCIATED WITH A1 [J].

FLASCHKA, H ;

NEWELL, AC ;

RATIU, T .

PHYSICA D, 1983, 9 (03) :324-332

← 1 2 →