Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation

DOI10.1016/j.jde.2022.09.015OpenAlexW4296638838MaRDI QIDQ2109357

Handan Borluk, Gabriel E. Bittencourt Moraes, Guilherme de Loreno, Gulcin M. Muslu, Fábio M. Amorin Natali

Publication date: 21 December 2022

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.08165

zbMATH Keywords

orbital stabilityfractional Schrödinger equationsmall-amplitude periodic wavesexistence and uniqueness of minimizers

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Traveling wave solutions (35C07) Fractional partial differential equations (35R11)

Related Items (1)

Stability of periodic waves for the defocusing fractional cubic nonlinear Schrödinger equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Well-posedness and ill-posedness for the cubic fractional Schrödinger equations
• Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\)
• The nonlinear Schrödinger equation. Singular solutions and optical collapse
• Nonlinear fractional Schrödinger equations in one dimension
• On the growth of Sobolev norms of solutions of the fractional defocusing NLS equation on the circle
• 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
• Stability theory of solitary waves in the presence of symmetry. II
• Theory of function spaces
• Orbital stability of standing waves for some nonlinear Schrödinger equations
• Stability theory of solitary waves in the presence of symmetry. I
• On a class of nonlinear Schrödinger equations
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Fractional quantum mechanics and Lévy path integrals
• Nondegeneracy and stability of antiperiodic bound states for fractional nonlinear Schrödinger equations
• On the continuum limit for discrete NLS with long-range lattice interactions
• The stability spectrum for elliptic solutions to the focusing NLS equation
• Orbital stability in the cubic defocusing NLS equation. I: Cnoidal periodic waves
• Stability of traveling wave solutions of nonlinear dispersive equations of NLS type
• On a fractional Schrödinger equation in the presence of harmonic potential
• The generalized fractional Benjamin-Bona-Mahony equation: analytical and numerical results
• Periodic waves in the fractional modified Korteweg-de Vries equation
• Existence of the global smooth solution to the period boundary value problem of fractional nonlinear Schrödinger equation
• Numerical generation of periodic traveling wave solutions of some nonlinear dispersive wave systems
• Orbital stability of periodic waves for the nonlinear Schrödinger equation
• Periodic traveling-wave solutions for regularized dispersive equations: sufficient conditions for orbital stability with applications
• Fractional Laplacian on the torus
• Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations
• Existence and Uniqueness theory for the fractional Schr\"odinger equation on the torus
• The Fourth-Order Dispersive Nonlinear Schrödinger Equation: Orbital Stability of a Standing Wave
• Variational Methods for Nonlocal Fractional Problems
• Modulational Stability of Ground States of Nonlinear Schrödinger Equations
• The Periodic Cubic Schrõdinger Equation
• Oscillation estimates of eigenfunctions via the combinatorics of noncrossing partitions
• Convergence of Petviashvili's Iteration Method for Numerical Approximation of Stationary Solutions of Nonlinear Wave Equations
• Stability of Periodic Waves of 1D Cubic Nonlinear Schrödinger Equations
• Waves of maximal height for a class of nonlocal equations with homogeneous symbols
• Stability of periodic waves for the fractional KdV and NLS equations
• An efficient method to compute solitary wave solutions of fractional Korteweg–de Vries equations
• On the stability of solitary wave solutions for a generalized fractional Benjamin–Bona–Mahony equation
• On some convergence results for fractional periodic Sobolev spaces
• Elliptic solutions of the defocusing NLS equation are stable
• The Orbital Stability of Elliptic Solutions of the Focusing Nonlinear Schrödinger Equation
• Convergence of Petviashvili's Method near Periodic Waves in the Fractional Korteweg--de Vries Equation
• Numerical study of fractional nonlinear Schrödinger equations
• Embedding Theorems and Quasi-Linear Elliptic Boundary Value Problems for Unbounded Domains

This page was built for publication: Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation