Authors
Citation
At. Ilichev, EXISTENCE OF A FAMILY OF SOLITON-LIKE SOLUTIONS FOR THE KAWAHARA EQUATION, Mathematical notes, 52(1-2), 1992, pp. 662-668
Citations number
13
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Mathematical notes
ISSN journal
10679073
→ ACNP
Volume
52
Issue
1-2
Year of publication
1992
Pages
662 - 668
Database
ISI
SICI code
0001-4346(1992)52:1-2<662:EOAFOS>2.0.ZU;2-R
Abstract
Existence is proved for a family of soliton-like solutions for the non
linear evolution equation u(t)+uu(x)+u(xxx)-u(xxxxx)=0. The problem is
reduced to investigating the fixed points of the operator (Au)(x) = i
ntegral-infinity/-infinity k(x-y)u2(y)dy. Integral-infinity/-infinity
k(x) = 1, whose action is considered in a cone of Frechet functions th
at are continuous on the real axis.