Asymptotic stability of solitons to 1D nonlinear Schrödinger equations in subcritical case

DOI10.1007/s11464-020-0857-6zbMath1465.35360arXiv1504.07826OpenAlexW3083536974MaRDI QIDQ2027119

Ze Li

Publication date: 25 May 2021

Published in: Frontiers of Mathematics in China (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.07826

zbMATH Keywords

asymptotic stabilitynonlinear Schrödinger equationsolitonsweak nonlinearity

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton solutions (35C08)

Related Items (1)

On selection of standing wave at small energy in the 1D cubic Schrödinger equation with a trapping potential

Cites Work

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• Stability of bound states of Hamiltonian PDEs in the degenerate cases
• On small energy stabilization in the NLS with a trapping potential
• The Hamiltonian structure of the nonlinear Schrödinger equation and the asymptotic stability of its ground states
• New estimates for a time-dependent Schrödinger equation
• On the growth of high Sobolev norms of solutions for KdV and Schrödinger equations
• Nonlinear scalar field equations. I: Existence of a ground state
• Stability theory of solitary waves in the presence of symmetry. II
• A centre-stable manifold for the focussing cubic NLS in \({\mathbb{R}}^{1+3\star}\)
• Non-generic blow-up solutions for the critical focusing NLS in 1-D
• An invariant set in energy space for supercritical NLS in 1D
• Asymptotic stability of small solitary waves to 1D nonlinear Schrödinger equations with potential
• Asymptotic stability of ground states in 3D nonlinear Schrödinger equation including subcritical cases
• Semigroups of linear operators and applications to partial differential equations
• Stability theory of solitary waves in the presence of symmetry. I
• Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations
• Nonlinear wave and Schrödinger equations. I: Instability of periodic and quasiperiodic solutions
• On asymptotic stability of solitary waves for nonlinear Schrödinger equations
• Stable manifolds for an orbitally unstable nonlinear Schrödinger equation
• On the asymptotic stability of bound states in 2D cubic Schrödinger equation
• Stability in \(H^1\) of the sum of \(K\) solitary waves for some nonlinear Schrödinger equations
• On asymptotic stability in energy space of ground states for nonlinear Schrödinger equations
• On the spectral properties ofL_±in three dimensions
• Asymptotic Stability of Multi-soliton Solutions for Nonlinear Schrödinger Equations
• A critical center-stable manifold for Schrödinger's equation in three dimensions
• Modulational Stability of Ground States of Nonlinear Schrödinger Equations
• Lyapunov stability of ground states of nonlinear dispersive evolution equations
• Uniform decay estimates and the lorentz invariance of the classical wave equation
• The nonlinear Schrödinger equation and the nonlinear heat equation reduction to linear form
• Global existence for nonlinear wave equations
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• Dispersive analysis of charge transfer models
• Stabilization of solutions to nonlinear Schrödinger equations
• Stable manifolds for all monic supercritical focusing nonlinear Schrödinger equations in one dimension
• SELECTION OF THE GROUND STATE FOR NONLINEAR SCHRÖDINGER EQUATIONS

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