PAINLEVE PROPERTY AND GROUP SYMMETRIES OF THE GENERALIZED KORTEWEG-DEVRIES EQUATION

Authors
ROLLINS DK SHIVAMOGGI BK
Citation
Dk. Rollins et Bk. Shivamoggi, PAINLEVE PROPERTY AND GROUP SYMMETRIES OF THE GENERALIZED KORTEWEG-DEVRIES EQUATION, Physica scripta. T, 49(3), 1994, pp. 261-263
Citations number
13
Categorie Soggetti
Physics
Journal title
Physica scripta. T → ACNP
ISSN journal
02811847
Volume
49
Issue
3
Year of publication
1994
Pages
261 - 263
Database
ISI
SICI code
0281-1847(1994)49:3<261:PPAGSO>2.0.ZU;2-#
Abstract
In this paper we consider some of the analytic properties of the gener alized Korteweg-de Vries equation u(t) + u(p)u(x) + u(xxx) = 0. We stu dy the Lie group symmetries of the equation and show that for p > 2 th ere is a three parameter group and if p = 1 or 2 the group has four pa rameters. The Painleve property is shown to be not satisfied when p > 2. The variational symmetries are also considered and are shown to lea d to the only three known conservation laws for general p.