Far field expansion for Hartree type equation

V. Georgiev; G. Venkov

doi:10.1063/1.4854775

Far field expansion for Hartree type equation

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We consider the scalar field equation -Δu(x)+(1|x|∗u2(x))u(x)-E2u(x)|x|+u(x) = 0 where u = u(|x|) is a radial positive solution and∗ is the convolution operator in R3. This equation can be rewritten as ordinary differential equation -ru"(r)-2u′(r)+r r∞(1s-1r)u2(s)s2dsu(r)+ru(r) = 0 and this note is concerned with asymptotic behavior at infinity of solutions of this equation.

Original language	English
Title of host publication	39th International Conference Applications of Mathematics in Engineering and Economics, AMEE 2013
Editors	George Venkov, Vesela Pasheva
Publisher	American Institute of Physics Inc.
Pages	343-355
Number of pages	13
ISBN (Electronic)	9780735411685
DOIs	https://doi.org/10.1063/1.4854775
Publication status	Published - 2013
Externally published	Yes
Event	39th International Conference on Applications of Mathematics in Engineering and Economics, AMEE 2013 - Sozopol, Bulgaria Duration: 2013 Jun 8 → 2013 Jun 13

Publication series

Name	AIP Conference Proceedings
Volume	1570
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Other

Other	39th International Conference on Applications of Mathematics in Engineering and Economics, AMEE 2013
Country/Territory	Bulgaria
City	Sozopol
Period	13/6/8 → 13/6/13

Keywords

Hartree equation
asymptotic behavior
exponential integral
solitary waves

ASJC Scopus subject areas

Physics and Astronomy(all)
Ecology, Evolution, Behavior and Systematics
Nature and Landscape Conservation
Plant Science
Ecology

Access to Document

10.1063/1.4854775

Cite this

Far field expansion for Hartree type equation. / Georgiev, V.; Venkov, G.
39th International Conference Applications of Mathematics in Engineering and Economics, AMEE 2013. ed. / George Venkov; Vesela Pasheva. American Institute of Physics Inc., 2013. p. 343-355 (AIP Conference Proceedings; Vol. 1570).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Georgiev, V & Venkov, G 2013, Far field expansion for Hartree type equation. in G Venkov & V Pasheva (eds), 39th International Conference Applications of Mathematics in Engineering and Economics, AMEE 2013. AIP Conference Proceedings, vol. 1570, American Institute of Physics Inc., pp. 343-355, 39th International Conference on Applications of Mathematics in Engineering and Economics, AMEE 2013, Sozopol, Bulgaria, 13/6/8. https://doi.org/10.1063/1.4854775

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AB - We consider the scalar field equation -Δu(x)+(1|x|∗u2(x))u(x)-E2u(x)|x|+u(x) = 0 where u = u(|x|) is a radial positive solution and∗ is the convolution operator in R3. This equation can be rewritten as ordinary differential equation -ru"(r)-2u′(r)+r r∞(1s-1r)u2(s)s2dsu(r)+ru(r) = 0 and this note is concerned with asymptotic behavior at infinity of solutions of this equation.

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Far field expansion for Hartree type equation

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Keywords

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