Riesz Potentials for Korteweg-de Vries Solitons and Sturm-Liouville Problems

Vladimir Varlamov

International Journal of Differential Equations, 2010, vol. 2010, 1-18

Abstract:

Riesz potentials (also called Riesz fractional derivatives) and their Hilbert transforms are computed for the Korteweg-de Vries soliton. They are expressed in terms of the full-range Hurwitz Zeta functions ð œ + ( ð ‘ , ð ‘Ž ) and ð œ âˆ’ ( ð ‘ , ð ‘Ž ) . It is proved that these Riesz potentials and their Hilbert transforms are linearly independent solutions of a Sturm-Liouville problem. Various new properties are established for this family of functions. The fact that the Wronskian of the system is positive leads to a new inequality for the Hurwitz Zeta functions.

Date: 2010
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJDE/2010/193893.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJDE/2010/193893.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:193893

DOI: 10.1155/2010/193893

Access Statistics for this article

More articles in International Journal of Differential Equations from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().