Stability of elliptic solutions to the defocusing fourth order nonlinear Schrodinger equation

被引：1

作者：

Sun, Wen-Rong ^{[1
]}

Liu, Meng-Meng ^{[1
]}

机构：

[1] Univ Sci & Technol Beijing, Sch Math & Phys, Beijing 100083, Peoples R China

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2023年 / 117卷

关键词：

Stability; 4NLS equation; Elliptic solutions; Subharmonic perturbations; Integrability; ORBITAL STABILITY; SOLITARY WAVES; CNOIDAL WAVES; DISPERSION;

D O I：

10.1016/j.cnsns.2022.106929

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the stability of elliptic solutions to the integrable defocusing fourth order nonlinear Schrodinger (4NLS) equation with respect to subharmonic perturbations. With the help of the squared-eigenfunction connection, we prove the spectral stability by relating the Lax spectrum to the stability spectrum. We establish the orbital stability of elliptic solutions to the 4NLS equation by constructing a Lyapunov functional. (c) 2022 Elsevier B.V. All rights reserved.

引用

页数：16

共 31 条

[1]

Ablowitz M.J., 1981, Solitons and the Inverse Scattering Transform

[2] Soliton, rational, and periodic solutions for the infinite hierarchy of defocusing nonlinear Schrodinger equations [J].

Ankiewicz, Adrian .

PHYSICAL REVIEW E, 2016, 94 (01)

[3]

Arnold V. I., 2013, Mathematical methods of classical mechanics

[4]

Arnold V. I., 1969, Amer. Math. Soc. Transl., V79, P267

[5] KDV CNOIDAL WAVES ARE SPECTRALLY STABLE [J].

Bottman, Nate ;

Deconinck, Bernard .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 25 (04) :1163-1180

[6] Elliptic solutions of the defocusing NLS equation are stable [J].

Bottman, Nathaniel ;

Deconinck, Bernard ;

Nivala, Michael .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2011, 44 (28)

[7] The Stability Analysis of the Periodic Traveling Wave Solutions of the mKdV Equation [J].

Deconinck, B. ;

Nivala, M. .

STUDIES IN APPLIED MATHEMATICS, 2011, 126 (01) :17-48

[8] THE ORBITAL STABILITY OF ELLIPTIC SOLUTIONS OF THE FOCUSING NONLINEAR SCHRODINGER EQUATION [J].

Deconinck, Bernard ;

Upsal, Jeremy .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2020, 52 (01) :1-41

[9] The stability spectrum for elliptic solutions to the sine-Gordon equation [J].

Deconinck, Bernard ;

McGill, Peter ;

Segal, Benjamin L. .

PHYSICA D-NONLINEAR PHENOMENA, 2017, 360 :17-35

[10] The stability spectrum for elliptic solutions to the focusing NLS equation [J].

Deconinck, Bernard ;

Segal, Benjamin L. .

PHYSICA D-NONLINEAR PHENOMENA, 2017, 346 :1-19

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