On three-wave interaction Schrödinger systems with quadratic nonlinearities: global well-posedness and standing waves

DOI10.3934/cpaa.2019100zbMath1483.35222OpenAlexW2930471041MaRDI QIDQ2069877

Ademir Pastor Ferreira

Publication date: 21 January 2022

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2019100

zbMATH Keywords

uniquenessSchrödinger equationsvariational methodspectral stabilitystanding-wave solutions

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Variational methods applied to PDEs (35A15) Variational methods for elliptic systems (35J50) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Soliton equations (35Q51) Lasers, masers, optical bistability, nonlinear optics (78A60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (6)

Blow-up solutions for a system of Schrödinger equations with general quadratic-type nonlinearities in dimensions five and six ⋮ Mass-transfer instability of ground-states for Hamiltonian Schrödinger systems ⋮ Scattering of radial solutions for quadratic-type Schrödinger systems in dimension five ⋮ Scattering for quadratic-type Schrödinger systems in dimension five without mass-resonance ⋮ A system of Schrödinger equations with general quadratic-type nonlinearities ⋮ Local and global theory for the three-wave mixing Schrödinger system with quadratic interactions on Zoll manifolds

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