Weakly coupled nonlinear Schrödinger systems: the saturation effect

DOI10.1007/s00526-011-0484-xzbMath1257.35171OpenAlexW2002002472MaRDI QIDQ1937820

Liliane de Almeida Maia, Benedetta Pellacci, Eugenio Montefusco

Publication date: 1 February 2013

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-011-0484-x

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) NLS equations (nonlinear Schrödinger equations) (35Q55) Positive solutions to PDEs (35B09)

Related Items (23)

Existence and multiplicity of nontrivial solutions of weakly coupled nonlinear Hartree type elliptic system ⋮ Existence and concentration of positive solutions to a fractional system with saturable term ⋮ Uniqueness of positive solutions for a class of Schrödinger systems with saturable nonlinearity ⋮ Solitary waves in nonlocal NLS with dispersion averaged saturated nonlinearities ⋮ Positive solutions for asymptotically linear problems in exterior domains ⋮ 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 ⋮ Existence and concentration of positive solutions for a system of coupled saturable Schrödinger equations ⋮ Normalized solutions for a coupled Schrödinger system with saturable nonlinearities ⋮ Spatiotemporal soliton interaction of saturable nonlinear Schrödinger equations in spatial dimensions higher than 1 ⋮ Localization of normalized solutions for saturable nonlinear Schrödinger equations ⋮ A positivity preserving iterative method for finding the ground states of saturable nonlinear Schrödinger equations ⋮ Periodic and asymptotically periodic quasilinear elliptic systems ⋮ Existence and concentration of ground states for saturable nonlinear Schrödinger equations with intensity functions in \(\mathbb{R}^2\) ⋮ Ground states of nonlinear Schrödinger systems with saturable nonlinearity in $\mathbb {R}^2$R2 for two counterpropagating beams ⋮ Ground states for a class of critical quasilinear coupled superlinear elliptic systems ⋮ Singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities ⋮ Orbital stability and energy estimate of ground states of saturable nonlinear Schrödinger equations with intensity functions in \(\mathbb{R}^2\) ⋮ Minimal Energy Solutions and Infinitely Many Bifurcating Branches for a Class of Saturated Nonlinear Schrödinger Systems ⋮ Coupled complex Ginzburg-Landau systems with saturable nonlinearity and asymmetric cross-phase modulation ⋮ Vectorial approach to coupled nonlinear Schrödinger systems under nonlocal Cauchy conditions ⋮ Normalized multi-bump solutions for saturable Schrödinger equations ⋮ Bound state for a strongly coupled nonlinear Schrödinger system with saturation ⋮ Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation

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