Asymptotic solutions of Hartree equations concentrated near low-dimensional submanifolds. I. The model with logarithmic singularity

DOI10.1070/IM2001V065N05ABEH000356zbMath1019.81018OpenAlexW2042037126MaRDI QIDQ4804414

A. V. Pereskokov, Mikhail V. Karasev

Publication date: 21 September 2003

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/im2001v065n05abeh000356

zbMATH Keywords

Wigner function Vlasov equation Airy polaron problem on quasimodes

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Many-body theory; quantum Hall effect (81V70) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30)

Related Items (7)

Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters ⋮ Semiclassical asymptotics of the spectrum near the lower boundary of spectral clusters for a Hartree-type operator ⋮ Semiclassical asymptotics of solutions to Hartree type equations concentrated on segments ⋮ Asymptotic solutions to the Hartree equation near a sphere. Asymptotics of self-consistent potentials ⋮ Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters ⋮ Asymptotics of the spectrum of a two-dimensional Hartree-type operator with a Coulomb self-action potential near the lower boundaries of spectral clusters ⋮ Asymptotics of the Hartree operator spectrum near the upper boundaries of spectral clusters: asymptotic solutions localized near a circle

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