A general review on the NLS equation with point-concentrated nonlinearity (Q6083155)

scientific article; zbMATH DE number 7757596

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English	A general review on the NLS equation with point-concentrated nonlinearity	scientific article; zbMATH DE number 7757596

Statements

instance of

scholarly article

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title

A general review on the NLS equation with point-concentrated nonlinearity (English)

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author

Lorenzo Tentarelli

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published in

Communications in Applied and Industrial Mathematics

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publication date

31 October 2023

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full work available at URL

https://arxiv.org/abs/2304.09086

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zbMATH Keywords

NLS equation

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concentrated nonlinearity

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Delta potentials

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well-posedness

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standing waves

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stability

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blow-up

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point-like limit

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MaRDI profile type

MaRDI publication profile

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cites work

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The dynamics of some quantum open systems with short-range nonlinearities

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Stability and symmetry-breaking bifurcation for the ground states of a NLS with a \(\delta ^{\prime}\) interaction

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Constrained energy minimization and ground states for NLS with point defects

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Fast Soliton Scattering by Attractive Delta Impurities

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Stability of standing waves for a nonlinear Schrödinger equation with a repulsive Dirac delta potential

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Nonlinear Schrödinger equation with a point defect

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Strong NLS soliton-defect interactions

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Fast soliton scattering by delta impurities

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Instability of bound states of a nonlinear Schrödinger equation with a Dirac potential

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Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations

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Ground states for the planar NLSE with a point defect as minimizers of the constrained energy

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Existence, structure, and robustness of ground states of a NLSE in 3D with a point defect

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Well posedness of the nonlinear Schrödinger equation with isolated singularities

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Failure of scattering for the NLSE with a point interaction in dimension two and three

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Blow-up and instability of standing waves for the NLS with a point interaction in dimension two

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A free particle on a circle with point interaction

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NLS ground states on the half-line with point interactions

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Competing nonlinearities in NLS equations as source of threshold phenomena on star graphs

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Prescribed mass ground states for a doubly nonlinear Schrödinger equation in dimension one

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Doubly nonlinear Schrödinger ground states on metric graphs

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Q3994511

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Time-dependent propagator with point interaction

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A class of nonlinear Schrödinger equations with concentrated nonlinearity

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Well-posedness of the two-dimensional nonlinear Schrödinger equation with concentrated nonlinearity

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The Cauchy problem for the Schrödinger equation in dimension three with concentrated nonlinearity

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The action of Volterra integral operators with highly singular kernels on Hölder continuous, Lebesgue and Sobolev functions

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Nonlinear singular perturbations of the fractional Schrödinger equation in dimension one

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The point-like limit for a NLS equation with concentrated nonlinearity in dimension three

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Stability of the standing waves of the concentrated NLSE in dimension two

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Orbital and asymptotic stability for standing waves of a nonlinear Schrödinger equation with concentrated nonlinearity in dimension three

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Stability theory of solitary waves in the presence of symmetry. I

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On Asymptotic Stability of Solitary Waves in Schrödinger Equation Coupled to Nonlinear Oscillator

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On asymptotic stability of solitons in a nonlinear Schrödinger equation

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Asymptotic stability for standing waves of a NLS equation with subcritical concentrated nonlinearity in dimension three: neutral modes

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Scattering for the 𝐿² supercritical point NLS

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The NLS equation in dimension one with spatially concentrated nonlinearities: the pointlike limit

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Identifiers

zbMATH Open document ID

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10.2478/caim-2023-0004

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6083155