Averaging of dispersion-managed solitons: Existence and stability

被引：22

作者：

Pelinovsky, DE ^{[1
]}

Zharnitsky, V

机构：

[1] McMaster Univ, Dept Math, Hamilton, ON L8S 4K1, Canada

[2] Lucent Technol, Bell Labs, Math Sci Res, Murray Hill, NJ 07974 USA

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2003年 / 63卷 / 03期

关键词：

existence and stability of pulses; optical solitons; dispersion management; averaging theory; normal form transformations; errors and convergence of asymptotic series; periodic NLS equation; integral NLS equation; Gaussian approximation;

D O I：

10.1137/S0036139902400477

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider existence and stability of dispersion-managed solitons in the two approximations of the periodic nonlinear Schrodinger (NLS) equation: (i) a dynamical system for a Gaussian pulse and (ii) an average integral NLS equation. We apply normal form transformations for finite-dimensional and infinite-dimensional Hamiltonian systems with periodic coefficients. First-order corrections to the leading-order averaged Hamiltonian are derived explicitly for both approximations. Bifurcations of soliton solutions and their stability are studied by analysis of critical points of the first-order averaged Hamiltonians. The validity of the averaging procedure is verified and the presence of ground states corresponding to dispersion-managed solitons in the averaged Hamiltonian is established.

引用

页码：745 / 776

页数：32

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