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 | |
| 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 |
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Keywords
- asymptotic behavior
- exponential integral
- Hartree equation
- solitary waves
ASJC Scopus subject areas
- Physics and Astronomy(all)
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
}
TY - GEN
T1 - Far field expansion for Hartree type equation
AU - Gueorguiev, Vladimir Simeonov
AU - Venkov, G.
PY - 2013/1/1
Y1 - 2013/1/1
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
UR - http://www.scopus.com/inward/record.url?scp=85061145838&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85061145838&partnerID=8YFLogxK
U2 - 10.1063/1.4854775
DO - 10.1063/1.4854775
M3 - Conference contribution
AN - SCOPUS:85061145838
VL - 1570
SP - 343
EP - 355
BT - 39th International Conference Applications of Mathematics in Engineering and Economics, AMEE 2013
A2 - Venkov, George
A2 - Pasheva, Vesela
PB - American Institute of Physics Inc.
ER -