Stationary solutions to cubic nonlinear Schrödinger equations with quasi-periodic boundary conditions

DOI10.1088/1751-8121/aba861OpenAlexW3045136368MaRDI QIDQ5870678

Andrea Sacchetti

Publication date: 23 January 2023

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.00803

zbMATH Keywords

nonlinear Schrödinger equationsJacobian elliptic functionsquasiperiodic boundary conditions

Mathematics Subject Classification ID

Quantum theory (81-XX) Statistical mechanics, structure of matter (82-XX)

Cites Work

• Stability of small periodic waves for the nonlinear Schrödinger equation
• Nonlinear stability of periodic traveling wave solutions to the Schrödinger and the modified Korteweg-de Vries equations
• The stability spectrum for elliptic solutions to the focusing NLS equation
• Orbital stability in the cubic defocusing NLS equation. I: Cnoidal periodic waves
• Periodic standing waves in the focusing nonlinear Schrödinger equation: rogue waves and modulation instability
• 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
• Analytic Properties of Bloch Waves and Wannier Functions
• Elliptic solutions of the defocusing NLS equation are stable
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