One-dimensional versions of three-dimensional system: Ground states for the NLS on the spatial grid
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Publication:5378092
zbMath1411.35262arXiv1811.01386MaRDI QIDQ5378092
Riccardo Adami, Simone Dovetta
Publication date: 11 June 2019
Full work available at URL: https://arxiv.org/abs/1811.01386
Variational inequalities (49J40) NLS equations (nonlinear Schrödinger equations) (35Q55) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) Special quantum systems, such as solvable systems (81Q80) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)
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Cites Work
- Threshold phenomena and existence results for NLS ground states on metric graphs
- On the lack of bound states for certain NLS equations on metric graphs
- Stationary nonlinear Schrödinger equation on simplest graphs
- NLS ground states on graphs
- NLS ground states on metric graphs with localized nonlinearities
- Negative energy ground states for the \(L^{2}\)-critical NLSE on metric graphs
- Existence of infinitely many stationary solutions of the \(L^{2}\)-subcritical and critical NLSE on compact metric graphs
- Variational and stability properties of constant solutions to the NLS equation on compact metric graphs
- Dimensional crossover with a continuum of critical exponents for NLS on doubly periodic metric graphs
- \(L^2\)-critical NLS on noncompact metric graphs with localized nonlinearity: topological and metric features
- Bound states of the NLS equation on metric graphs with localized nonlinearities
- Bifurcations and stability of standing waves in the nonlinear Schrödinger equation on the tadpole graph
- Nonlinear Schrödinger equation on graphs: recent results and open problems
- FAST SOLITONS ON STAR GRAPHS
- Existence of dynamics for a 1D NLS equation perturbed with a generalized point defect
- Nonlinear dynamics on branched structures and networks
- Ground States of the L 2-Critical NLS Equation with Localized Nonlinearity on a Tadpole Graph
