Orbital stability of standing waves for a system of nonlinear Schrödinger equations with three wave interaction

DOI10.1016/J.NA.2017.10.013zbMath1379.35285arXiv1709.09788OpenAlexW2760295286MaRDI QIDQ1683046

Alex H. Ardila

Publication date: 6 December 2017

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.09788

zbMATH Keywords

solitary waveorbital stabilitynonlinear Schrödinger system

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Variational methods applied to PDEs (35A15) NLS equations (nonlinear Schrödinger equations) (35Q55) Lasers, masers, optical bistability, nonlinear optics (78A60) Statistical mechanics of plasmas (82D10) Soliton solutions (35C08)

Related Items (14)

Existence of a minimizer for a nonlinear Schrödinger system with three wave interaction under non-symmetric potentials ⋮ On a system of nonlinear Schrödinger equations with quadratic interaction and L2-critical growth ⋮ Variational problems associated with a system of nonlinear Schrödinger equations with three wave interaction ⋮ A singular perturbation problem for a nonlinear Schrödinger system with three wave interaction ⋮ Unnamed Item ⋮ Infinite sharp conditions by Nehari manifolds for nonlinear Schrödinger equations ⋮ Solving elliptic Schrödinger systems with control constraints ⋮ Explicit solutions of cylindrical Schrödinger equation with radial potentials ⋮ Ground state solutions for a non-autonomous nonlinear Schrödinger-KdV system ⋮ Existence, stability of standing waves and the characterization of finite time blow-up solutions for a system NLS with quadratic interaction ⋮ Asymptotic expansion of the ground state energy for nonlinear Schrödinger system with three wave interaction ⋮ Energy asymptotic expansion for a system of nonlinear Schrödinger equations with three wave interaction ⋮ Existence and convergence results of meromorphic solutions to the equilibrium system with angular velocity ⋮ The compactness of minimizing sequences for a nonlinear Schrödinger system with potentials

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