Blow-up and strong instability of standing waves for the NLS-\(\delta\) equation on a star graph

DOI10.1016/j.na.2020.111753zbMath1464.35322arXiv1908.07122OpenAlexW3007418669WikidataQ122112561 ScholiaQ122112561MaRDI QIDQ1988382

Masahito Ohta, Nataliia Goloshchapova

Publication date: 23 April 2020

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.07122

zbMATH Keywords

nonlinear Schrödinger equationstar graphstanding wavevirial identitystrong instability\(\delta\)- and \(\delta^\prime\)-interaction

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) General theory of ordinary differential operators (47E05) NLS equations (nonlinear Schrödinger equations) (35Q55) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Blow-up in context of PDEs (35B44) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items

Competing nonlinearities in NLS equations as source of threshold phenomena on star graphs ⋮ Standing waves on quantum graphs ⋮ Variational and stability properties of coupled NLS equations on the star graph ⋮ Blow-up and instability of standing waves for the NLS with a point interaction in dimension two ⋮ Standing waves of the quintic NLS equation on the tadpole graph ⋮ Failure of scattering to standing waves for a Schrödinger equation with long-range nonlinearity on star graph ⋮ Dynamical and variational properties of the NLS-\( \delta'_s\) equation on the star graph ⋮ Instability of ground states for the NLS equation with potential on the star graph ⋮ Secondary bifurcations in semilinear ordinary differential equations

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