Sreelatha, K S; Dr.Babu, Joseph K(Cochin University of Science And Technology, June , 1990)
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Abstract:
Usually typical dynamical systems are non integrable. But
few systems of practical interest are integrable. The soliton concept is a
sophisticated mathematical construct based on the integrability of a class ol'
nonlinear differential equations. An important feature in the clevelopment.
of the theory of solitons and of complete integrability has been the interplay
between mathematics and physics. Every integrable system has a lo11g list
of special properties that hold for integrable equations and only for them.
Actually there is no specific definition for integrability that is suitable for all cases.
.There exist several integrable partial clillerential equations( pdes)
which can be derived using physically meaningful asymptotic teclmiques
from a very large class of pdes. It has been established that many 110nlinear
wa.ve equations have solutions of the soliton type and the theory of
solitons has found applications in many areas of science. Among these,
well-known equations are Korteweg de-Vries(KdV), modified KclV, Nonlinear
Schr6dinger(NLS), sine Gordon(SG) etc..These are completely integrable
systems. Since a small change in the governing nonlinear prle may cause the
destruction of the integrability of the system, it is interesting to study the
effect of small perturbations in these equations. This is the motivation of the
present work.
Description:
Department of physics, Cochin University of Science And Technology