On the Stability of the Periodic Waves for the Benney System

DOI10.1137/21M1461630zbMath1492.35308arXiv2204.01628MaRDI QIDQ5090121

Milena Stanislavova, Sevdzhan A. Hakkaev, Atanas G. Stefanov

Publication date: 15 July 2022

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.01628

zbMATH Keywords

spectral stabilityperiodic wavesBenney system

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Boundary value problems for nonlinear higher-order PDEs (35G30) NLS equations (nonlinear Schrödinger equations) (35Q55)

Cites Work

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• Unnamed Item
• Orbital stability for periodic standing waves of the Klein-Gordon-Zakharov system and the beam equation
• The orbital stability of the cnoidal waves of the Korteweg-de Vries equation
• Orbital instability of standing waves for the quadratic-cubic Klein-Gordon-Schrödinger system
• Well posedness and stability in the periodic case for the Benney system
• Orbital stability of periodic waves for the Klein-Gordon-Schrödinger system
• Stability of small periodic waves for the nonlinear Schrödinger equation
• Ill-Posedness for the Benney system
• Nonlinear stability of periodic traveling wave solutions to the Schrödinger and the modified Korteweg-de Vries equations
• Stability of cnoidal waves
• Stability properties of periodic standing waves for the Klein-Gordon-Schrödinger system
• On the periodic Schrödinger-Boussinesq system
• The modulational instability for a generalized Korteweg-de Vries equation
• Stability and instability of periodic travelling wave solutions for the critical Korteweg-de Vries and nonlinear Schrödinger equations
• Interaction equations for short and long dispersive waves
• Spectral and dynamical stability of nonlinear waves
• An instability index theory for quadratic pencils and applications
• Orbital stability of periodic waves for the nonlinear Schrödinger equation
• On the Spectral and Orbital Stability of Spatially Periodic Stationary Solutions of Generalized Korteweg-de Vries Equations
• An index theorem for the stability of periodic travelling waves of Korteweg–de Vries type
• Positivity Properties of the Fourier Transform and the Stability of Periodic Travelling-Wave Solutions
• Stability of periodic optical solitons for a nonlinear Schrödinger system
• Modulational Stability of Ground States of Nonlinear Schrödinger Equations
• Significant Interactions Between Small and Large Scale Surface Waves
• A General Theory for Interactions Between Short and Long Waves
• Orbital stability of solitary waves of the long wave-short wave resonance equations
• On a nonlinear Schrödinger equation arising in the theory of water waves
• Nonlinear Stability of Periodic Traveling Wave Solutions of the Generalized Korteweg–de Vries Equation
• Linear stability analysis for periodic travelling waves of the Boussinesq equation and the Klein–Gordon–Zakharov system
• Inertia law for spectral stability of solitary waves in coupled nonlinear Schrödinger equations
• Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems
• Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems

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