Linear Instability of Breathers for the Focusing Nonlinear Schrodinger Equation

被引：16

作者：

Haragus, Mariana ^{[1
]}

Pelinovsky, Dmitry E. ^{[2
]}

机构：

[1] Univ Bourgogne Franche Comte, FEMTO ST Inst, CNRS, 15b Ave Montboucons, F-25030 Besancon, France

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

来源：

JOURNAL OF NONLINEAR SCIENCE | 2022年 / 32卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Nonlinear Schrodinger equation; Breathers; Linear instability; Darboux transformation; Lax spectrum; Zakharov-Shabat spectral problems; ROGUE WAVES; STABILITY; OPTICS;

D O I：

10.1007/s00332-022-09819-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Relying upon tools from the theory of integrable systems, we discuss the linear instability of the Kuznetsov-Ma breathers and the Akhmediev breathers of the focusing nonlinear Schrodinger equation. We use the Darboux transformation to construct simultaneously the breathers and the exact solutions of the Lax system associated with the breathers. We obtain a full description of the Lax spectra for the two breathers, including multiplicities of eigenvalues. Solutions of the linearized NLS equations are then obtained from the eigenfunctions and generalized eigenfunctions of the Lax system. While we do not attempt to prove completeness of eigenfunctions, we aim to determine the entire set of solutions of the linearized NLS equations generated by the Lax system in appropriate function spaces.

引用

页数：40

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