Far field expansion for Hartree type equation

Vladimir Simeonov Gueorguiev; 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
Volume	1570
ISBN (Electronic)	9780735411685
DOIs	https://doi.org/10.1063/1.4854775
Publication status	Published - 2013 Jan 1
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

Other

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

Keywords

asymptotic behavior
exponential integral
Hartree equation
solitary waves

ASJC Scopus subject areas

Physics and Astronomy(all)

Access to Document

10.1063/1.4854775

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Cite this

Far field expansion for Hartree type equation. / Gueorguiev, Vladimir Simeonov; Venkov, G.

39th International Conference Applications of Mathematics in Engineering and Economics, AMEE 2013. ed. / George Venkov; Vesela Pasheva. Vol. 1570 American Institute of Physics Inc., 2013. p. 343-355.

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

Gueorguiev, VS & 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. 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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N2 - 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.

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.

KW - asymptotic behavior

KW - exponential integral

KW - Hartree equation

KW - solitary waves

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