Symmetry operators of a Hartree-type equation with quadratic potential; Siberian Mathematical Journal; Vol. 46, iss. 1

Symmetry operators of a Hartree-type equation with quadratic potential; Siberian Mathematical Journal; Vol. 46, iss. 1

Bibliographic Details
Parent link:	Siberian Mathematical Journal: Scientific Journal Vol. 46, iss. 1.— 2005.— [P. 119-132]
Main Author:	Lisok A. L. Aleksandr Leonidovich
Other Authors:	Trifonov A. Yu. Andrey Yurievich, Shapovalov A. V. Aleksandr Vasilyevich
Summary:	Title screen We study the symmetry properties of a nonstationary one-dimensional Hartree-type equation with quadratic periodic potential and nonlocal nonlinearity. We find an explicit form of a nonlinear evolution operator for this equation and obtain a solution to a Cauchy problem in the class of semiclassically concentrated functions. We find parametric families of nonlinear symmetry operators of a Hartree-type equation (keeping invariant the set of solutions to this equation). Using the symmetry operators, we construct families of exact solutions to the equation. This approach constructively extends the ideas and methods of group analysis to the case of nonlinear integro-differential equations Режим доступа: по договору с организацией-держателем ресурса
Language:	English
Published:	2005
Subjects:	электронный ресурс труды учёных ТПУ nonlinear equations semiclassical asymptotics Hartree-type equation evolution operator symmetry operators semiclassical concentrated states
Online Access:	http://dx.doi.org/10.1007/s11202-005-0013-2
Format:	xMaterials Electronic Book Chapter
KOHA link:	https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=636515

Similar Items

Green's Function of a Hartree-Type Equation with a Quadratic Potential; Theoretical and Mathematical Physics; Vol. 141, iss. 2
by: Lisok A. L. Aleksandr Leonidovich
Published: (2004)

Exact Solutions and Symmetry Operators for the Nonlocal Gross-Pitaevskii Equation with Quadratic Potential; Symmetry, Integrability and Geometry: Methods and Applications (SIGMA); Vol. 1
by: Shapovalov A. V. Aleksandr Vasilyevich
Published: (2005)

Formalism of semiclassical asymptotics for a two-component Hartree-type equation; Russian Physics Journal; Vol. 52, iss. 10
by: Smirnova E. I.
Published: (2009)

Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation; Symmetry, Integrability and Geometry: Methods and Applications (SIGMA); Vol. 1
by: Borisov A. V. Aleksey Vladimirovich
Published: (2005)

Semiclassical Spectral Series Localized on a Curve for the Gross–Pitaevskii Equation with a Nonlocal Interaction; Symmetry; Vol. 13, iss. 7
by: Kulagin A. E. Anton Evgenievich
Published: (2021)

Nonlinear Fokker-Planck Equation in the Model of Asset Returns; Symmetry, Integrability and Geometry: Methods and Applications (SIGMA); Vol. 4
by: Shapovalov A. V. Aleksandr Vasilyevich
Published: (2008)

An application of the Maslov complex germ method to the one-dimensional nonlocal Fisher–KPP equation; International Journal of Geometric Methods in Modern Physics; Vol. 15, iss. 6
by: Shapovalov A. V. Aleksandr Vasilyevich
Published: (2018)

Symmetry Operators for the Fokker-Plank-Kolmogorov Equation with Nonlocal Quadratic Nonlinearity; Symmetry, Integrability and Geometry: Methods and Applications (SIGMA); Vol. 3
by: Shapovalov A. V. Aleksandr Vasilyevich
Published: (2007)

Semiclassical approximation for the twodimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation with nonlocal nonlinearity in polar coordinates; Russian Physics Journal; Vol. 53, iss. 12
by: Trifonov A. Yu. Andrey Yurievich
Published: (2011)

Symmetries of the Fisher–Kolmogorov–Petrovskii–Piskunov equation with a nonlocal nonlinearity in a semiclassical approximation; Journal of Mathematical Analysis and Applications; Vol. 395, iss. 2
Published: (2012)

The one-dimensional Fisher–Kolmogorov equation with a nonlocal nonlinearity in a semiclassical approximation; Russian Physics Journal; Vol. 52, iss. 9
by: Trifonov A. Yu. Andrey Yurievich
Published: (2009)

The Gross–Pitaevskii Equation with a Nonlocal Interaction in a Semiclassical Approximation on a Curve; Symmetry; Vol. 12, iss. 2
by: Shapovalov A. V. Aleksandr Vasilyevich
Published: (2020)

Modulation of the velocity of soliton-like perturbations for the sine–Gordon equation with external force and dissipation; Russian Physics Journal; Vol. 52, iss. 12
by: Krasnobaeva L. A.
Published: (2009)

Family of Asymptotic Solutions to the Two-Dimensional Kinetic Equation with a Nonlocal Cubic Nonlinearity; Symmetry; Vol. 14, iss. 3
by: Shapovalov A. V. Aleksandr Vasiljevich
Published: (2022)

A Semiclassical Approach to the Nonlocal Nonlinear Schrödinger Equation with a Non-Hermitian Term; Mathematics; Vol. 12, iss. 4
by: Kulagin A. E. Anton Evgenievich
Published: (2024)

Symmetry operators and separation of variables in the (2+1)-dimensional Dirac equation with external electromagnetic field; International Journal of Geometric Methods in Modern Physics; Vol. 15, iss. 5
by: Shapovalov A. V. Aleksandr Vasilyevich
Published: (2018)

One-Dimensional Fokker–Planck Equation with Quadratically Nonlinear Quasilocal Drift; Russian Physics Journal; Vol. 60, iss. 12
by: Shapovalov A. V. Aleksandr Vasilyevich
Published: (2018)

Symmetries of the One-Dimensional Fokker–Planck–Kolmogorov Equation with a Nonlocal Quadratic Nonlinearity; Russian Physics Journal; Vol. 60, iss. 2
by: Levchenko E. A. Evgeny Anatolievich
Published: (2017)

Approximate Solutions and Symmetry of a Two-Component Nonlocal Reaction-Diffusion Population Model of the Fisher-KPP Type; Symmetry; Vol. 11, iss. 3
by: Shapovalov A. V. Aleksandr Vasiljevich
Published: (2019)

Conservation laws for two-phase filtration models; Communications in Nonlinear Science and Numerical Simulation; Vol. 19, iss. 2
Published: (2014)

On two-dimensional integrable models with a cubic or quartic integral of motion; Journal of High Energy Physics; № 9
by: Galajinsky A. V. Anton Vladimirovich
Published: (2013)

On the First Eigenvalue of the Degenerate pp -Laplace Operator in Non-convex Domains; Integral Equations and Operator Theory; Vol. 90, iss. 4
by: Gol’dshtein V. M. Vladimir
Published: (2018)

Discrete Dynamics Basic Theory and Examples /
by: Bacciotti, Andrea
Published: (2022)

Асимптотика решения сингулярно возмущенной задачи с периодическими точками поворота в комплексной плоскости; Известия Томского политехнического университета [Известия ТПУ]; Т. 324, № 2 : Математика и механика. Физика
by: Турсунов Д. А. Дилмурат Абдиллажанович
Published: (2014)

Асимптотика решения бисингулярно возмущенного эллиптического уравнения. Случай особой точки на границе; Известия Томского политехнического университета [Известия ТПУ]; Т. 324, № 2 : Математика и механика. Физика
by: Турсунов Д. А. Дилмурат Абдиллажанович
Published: (2014)

Sobolev extension operators and Neumann eigenvalues; Journal of Spectral Theory; Vol. 10, iss. 1
by: Goldshteyn V. M. Vladimir Mikhaylovich
Published: (2020)

Formation regularities of secondary electrons spectrum while interacting heavy-current electric beam with gases; Modern Techniques and Technology (MTT' 2000)
by: Daneykin (Daneikin) Yu. V. Yuri Viktorovich
Published: (2000)

Quasianalytical solution of inhomogeneous differential equation with cubic nonlinearity; Advances in Computer Science Research; Vol. 72 : Information technologies in Science, Management, Social sphere and Medicine (ITSMSSM 2017)
by: Inkhireeva T.
Published: (2017)

Semiclassical spectral series of the two-component Hartree-type operator; Russian Physics Journal; Vol. 50, iss. 5
Published: (2007)

Generation and removal of apparent singularities in linear ordinary differential equations with polynomial coefficients; Theoretical and Mathematical Physics; Vol. 189, iss. 3
Published: (2016)

The research of uranium monoxide-oxide dissolution process in nitric acid; Bulletin of the Tomsk Polytechnic University; Vol. 311, № 3
Published: (2007)

The problem of the number of integer points in families of anisotropically expanding domains, with applications to spectral theory; Mathematical Notes; Vol. 92, iss. 3-4
by: Kordyukov Yu. A. Yuri Arkadievich
Published: (2012)

New insight into WDVV equation; Journal of High Energy Physics; Vol. 71, № 4
by: Galajinsky A. V. Anton Vladimirovich
Published: (2004)

Semiclassical Approach to the Nonlocal Kinetic Model of Metal Vapor Active Media; Mathematics; Vol. 9, iss. 23
by: Shapovalov A. V. Aleksandr Vasiljevich
Published: (2021)

Нелинейное алгебраическое оценивание индуктивности вибрационного электромагнитного активатора по кривой затухания тока; Известия Томского политехнического университета [Известия ТПУ]. Инжиниринг георесурсов; Т. 331, № 1
Published: (2020)

Control of Wave and Beam PDEs The Riesz Basis Approach /
by: Guo, Bao-Zhu, et al.
Published: (2019)

A conditionally integrable bi-confluent Heun potential involving inverse square root and centrifugal barrier terms; Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences; Vol. 73, iss. 5
by: energy spectrum T. A. Tigran Arturovich
Published: (2018)

Recent Advances in Intuitionistic Fuzzy Logic Systems Theoretical Aspects and Applications /
Published: (2019)

The evolution operator of the Hartree-type equation with a quadratic potential; Journal of Physics A: Mathematical and General; Vol. 37, iss. 16
by: Lisok A. L. Aleksandr Leonidovich
Published: (2004)

Chaos, Complexity and Leadership 2016
Published: (2018)