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International Journal of Modern Physics C
c World Scientific Publishing Company
INTEGRABILITY OF A NON-AUTONOMOUS
COUPLED KdV SYSTEM
AYS¸E KARASU(KALKANLI) and TUBA KILIC¸
Department of Physics, Middle East Technical University
06531 Ankara, Turkey
Received (received date)
Revised (revised date)
The Painlev´e property of coupled, non-autonomous Korteweg-de Vries (KdV) type of
systems is studied. The conditions under which the systems pass the Painlev´e test for
integrability are obtained. For some of the integrable cases, exact solutions are given.
Keywords : non-autonomous KdV systems; Painlev´e analysis; exact solutions
1. Introduction
For a better understanding of complicated physical phenomena scientists have expe-
rienced that it is necessary to introduce mathematical models whose time evolutions
might show some features very similar to those of the original phenomena. These
models are usually systems of nonlinear differential equations. These equations can
be solved by the use of approximation techniques. But the range of applicability
and usefulness of these solutions increase the interest on the exact solutions and
on the solution generating methods for nonlinear equations. Before attempting to
solve an equation one usually needs to know whether the equation is integrable or
not. The difficulty of obtaining solutions by use of inverse scattering transform
technique, makes this information valuable. One of the powerful tools to obtain
this information is the Painlev´e test for integrability. There are strong evidences
that all integrable equations have Painlev´e
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