Far field expansion for Hartree type equation

Vladimir Simeonov Gueorguiev; G. Venkov

doi:10.1063/1.4854775

Far field expansion for Hartree type equation

研究成果: Conference contribution

抄録

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.

本文言語	English
ホスト出版物のタイトル	39th International Conference Applications of Mathematics in Engineering and Economics, AMEE 2013
編集者	George Venkov, Vesela Pasheva
出版社	American Institute of Physics Inc.
ページ	343-355
ページ数	13
巻	1570
ISBN（電子版）	9780735411685
DOI	https://doi.org/10.1063/1.4854775
出版ステータス	Published - 2013 1月 1
外部発表	はい
イベント	39th International Conference on Applications of Mathematics in Engineering and Economics, AMEE 2013 - Sozopol, Bulgaria 継続期間: 2013 6月 8 → 2013 6月 13

Other

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

ASJC Scopus subject areas

物理学および天文学（全般）

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10.1063/1.4854775

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引用スタイル

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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title = "Far field expansion for Hartree type equation",

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.",

keywords = "asymptotic behavior, exponential integral, Hartree equation, solitary waves",

author = "Gueorguiev, {Vladimir Simeonov} and G. Venkov",

year = "2013",

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doi = "10.1063/1.4854775",

language = "English",

volume = "1570",

pages = "343--355",

editor = "George Venkov and Vesela Pasheva",

booktitle = "39th International Conference Applications of Mathematics in Engineering and Economics, AMEE 2013",

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note = "39th International Conference on Applications of Mathematics in Engineering and Economics, AMEE 2013 ; Conference date: 08-06-2013 Through 13-06-2013",

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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

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DO - 10.1063/1.4854775

M3 - Conference contribution

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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.

T2 - 39th International Conference on Applications of Mathematics in Engineering and Economics, AMEE 2013

Y2 - 8 June 2013 through 13 June 2013

ER -

Far field expansion for Hartree type equation

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