Far field expansion for Hartree type equation

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish
Title of host publication39th International Conference Applications of Mathematics in Engineering and Economics, AMEE 2013
EditorsGeorge Venkov, Vesela Pasheva
PublisherAmerican Institute of Physics Inc.
Pages343-355
Number of pages13
Volume1570
ISBN (Electronic)9780735411685
DOIs
Publication statusPublished - 2013 Jan 1
Externally publishedYes
Event39th International Conference on Applications of Mathematics in Engineering and Economics, AMEE 2013 - Sozopol, Bulgaria
Duration: 2013 Jun 82013 Jun 13

Other

Other39th International Conference on Applications of Mathematics in Engineering and Economics, AMEE 2013
CountryBulgaria
CitySozopol
Period13/6/813/6/13

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Keywords

  • asymptotic behavior
  • exponential integral
  • Hartree equation
  • solitary waves

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Gueorguiev, V. S., & 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, pp. 343-355). American Institute of Physics Inc.. https://doi.org/10.1063/1.4854775