Stability theory for the NLS equation on looping edge graphs

General theory of ordinary differential operators (47E05) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Time-dependent Schrödinger equations and Dirac equations (35Q41) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Cites Work

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Stable standing waves for a NLS on star graphs as local minimizers of the constrained energy
Threshold phenomena and existence results for NLS ground states on metric graphs
Parabolic theory of the discrete \(p\)-Laplace operator
NLS ground states on graphs
Harmonic analysis on inhomogeneous amenable networks and the Bose-Einstein condensation
Negative energy ground states for the \(L^{2}\)-critical NLSE on metric graphs
Variational properties and orbital stability of standing waves for NLS equation on a star graph
Stability theory of solitary waves in the presence of symmetry. II
Sufficient conditions for stability of solitary-wave solutions of model equations for long waves
Stability theory of solitary waves in the presence of symmetry. I
Dependence of the \(n\)th Sturm-Liouville eigenvalue on the problem
Extension theory approach in the stability of the standing waves for the NLS equation with point interactions on a star graph
Multiple positive bound states for the subcritical NLS equation on metric graphs
On the orbital instability of excited states for the NLS equation with the \(\delta\)-interaction on a star graph
Nonlinear Schrödinger equations on periodic metric graphs
On the ground state of quantum graphs with attractive \(\delta \)-coupling
Standing waves of the quintic NLS equation on the tadpole graph
Instability of static solutions of the sine-Gordon equation on a \(\mathcal{Y}\)-junction graph with \(\delta\)-interaction
Instability theory of kink and anti-kink profiles for the sine-Gordon equation on Josephson tricrystal boundaries
Unstable kink and anti-kink profile for the sine-Gordon equation on a \({\mathcal{Y}} \)-junction graph
Standing waves on a flower graph
A reduced model of pulsatile flow in an arterial compartment
Ground State on the Dumbbell Graph
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
Linear instability criterion for the Korteweg–de Vries equation on metric star graphs
Standing waves on quantum graphs
Orbital stability of standing waves for supercritical NLS with potential on graphs
Drift of Spectrally Stable Shifted States on Star Graphs
Existence of the ground state for the NLS with potential on graphs
Ground state and orbital stability for the NLS equation on a general starlike graph with potentials
Quantum graphs: I. Some basic structures
Stability theory for two-lobe states on the tadpole graph for the NLS equation

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