Systems of nonlinear Schrödinger equations. A survey

DOI10.4171/RLM/535zbMath1167.35362MaRDI QIDQ2390610

Antonio Ambrosetti

Publication date: 31 July 2009

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

zbMATH Keywords

variational methodsperturbation methodsnonlinear Schrödinger equations and systems

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) NLS equations (nonlinear Schrödinger equations) (35Q55) Variational methods for second-order elliptic equations (35J20)

Related Items (3)

Existence and concentration of positive solutions for a system of coupled saturable Schrödinger equations ⋮ Nonlinear ellipticity on unbounded domains ⋮ On finding the ground state solution to the linearly coupled Brezis-Nirenberg system in high dimensions: the cooperative case

Cites Work

• Positive solutions for a weakly coupled nonlinear Schrödinger system
• Solitons of linearly coupled systems of semilinear non-autonomous equations on \(\mathbb R^{n}\)
• Remarks on some systems of nonlinear Schrödinger equations
• Multipulse phases in k-mixtures of Bose-Einstein condensates
• Positive solutions of some nonlinear elliptic problems in exterior domains
• The effect of concentrating potentials in some singularly perturbed problems
• On concentration of positive bound states of nonlinear Schrödinger equations
• On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potential
• Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
• Local mountain passes for semilinear elliptic problems in unbounded domains
• Least energy solitary waves for a system of nonlinear Schrödinger equations in \({\mathbb{R}^n}\)
• Coupled nonlinear Schrödinger systems with potentials
• Multi-bump solitons to linearly coupled systems of nonlinear Schrödinger equations
• Multi-peak periodic semiclassical states for a class of nonlinear Schrödinger equations
• On Concentration of Positive Bound States of Nonlinear Schrödinger Equations with Competing Potential Functions
• Novel soliton states and bifurcation phenomena in nonlinear fiber couplers
• Existence of multi-bumb solutions for nonlinear schrödinger equations via variational method

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