Orbital stability and energy estimate of ground states of saturable nonlinear Schrödinger equations with intensity functions in \(\mathbb{R}^2\)

DOI10.1016/j.jde.2017.05.030zbMath1375.35498OpenAlexW2626758038MaRDI QIDQ2013914

Yanyan Li

Publication date: 10 August 2017

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

Full work available at URL: https://doi.org/10.1016/j.jde.2017.05.030

zbMATH Keywords

Schrödinger equationsenergy estimateorbital stabilityground statessaturable nonlinearityconvexity argument

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Estimates of eigenvalues in context of PDEs (35P15) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (7)

Newton--Noda Iteration for Computing the Ground States of Nonlinear Schrödinger Equations ⋮ Localization of normalized solutions for saturable nonlinear Schrödinger equations ⋮ A positivity preserving iterative method for finding the ground states of saturable nonlinear Schrödinger equations ⋮ Exciting rogue waves, breathers, and solitons in coherent atomic media ⋮ Multiple positive solutions of saturable nonlinear Schrödinger equations with intensity functions ⋮ Existence and concentration of ground states for saturable nonlinear Schrödinger equations with intensity functions in \(\mathbb{R}^2\) ⋮ Normalized multi-bump solutions for saturable Schrödinger equations

Cites Work

• Unnamed Item
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• Proprietà di alcune classi di funzioni in più variabili
• Nonlinear scalar field equations. I: Existence of a ground state
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• The second order upper bound for the ground energy of a Bose gas
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• Orbital stability of standing waves for some nonlinear Schrödinger equations
• The virial theorem and ground state energy estimates of nonlinear Schrödinger equations in \(\mathbb{R}^2\) with square root and saturable nonlinearities in nonlinear optics
• Minimax theorems
• Weakly coupled nonlinear Schrödinger systems: the saturation effect
• Singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities
• Ground states of nonlinear Schrödinger systems with saturable nonlinearity in $\mathbb {R}^2$R2 for two counterpropagating beams

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