Integro-differential equation of non-local wave interaction

Journal Article · Sat Jun 30 00:00:00 EDT 2007 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2007V198N06ABEH003863; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21267060

Engibaryan, N B; Khachatryan, Aghavard Kh ^[1]

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1. Institute of Mathematics, Academy of Sciences of Armenia, Erevan (Armenia)

The integro-differential equation d{sup 2}f/dx{sup 2} + Af = {integral}{sub 0}{sup {infinity}}K(x-t)f(t)dt + g(x) with kernel K(x)={lambda}{integral}{sub a}{sup {infinity}}e{sup -|x|p}G(p)dp, a{>=}0, is considered, in which A>0, {lambda} element of 9-{infinity},{infinity}), G(p){>=}0, 2{integral}{sub a}{sup {infinity}}1/p g(p)dp=1. These equations arise, in particular, in the theory of non-local wave interaction. A factorization method of their analysis and solution is developed. Bibliography: 9 titles.

• OSTI ID: 21267060
• Journal Information: Sbornik. Mathematics, Vol. 198, Issue 6; Other Information: DOI: 10.1070/SM2007v198n06ABEH003863; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
FACTORIZATION
INTEGRO-DIFFERENTIAL EQUATIONS
WAVE FUNCTIONS