\centerline{\bf A Numerical Treatment of K(2,3) Kdv Type Equation}
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\centerline{\bf M. S. Ismail}

\centerline{Department of Mathematics}

\centerline{College of Science}

\centerline{P.O.Box 9028}

\centerline{Jeddah-21413}

\centerline{Saudi Arabia}

\centerline{E-mail SCF 3005 @ KAAU.EDU.SA}
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{\bf Keywords: Finite difference  method, PDEs, Compacton}
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\centerline{\bf ABSTRACT}
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The Koetewege-de Vries (Kdv) equation has recently been
generalized by Rosenau and Hyman �1� to a class of partial differential
equations (PDEs) which has solitary wave solution with
compact support. These solitary wave solutions are called compactons. Compactons
are solitary waves with
the remarkable soliton property, that after colliding with other compactons,
they reemerge with the same
coherent shape. These particle-like waves exhibit elastic collision that are
similar to the soliton interaction
associated with completely integrable systems. The point where two compactons
collide is marked by a creation of low amplitude
compacton-anti compacton pairs. These equations have only a finite number of
local conservation Laws.
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\par In this paper, an implicit Numerical solution has been developed
to solve the K(2,3) equation. Accuracy and stability of the method have
been studied. The analytical solution and the conserved quantities are
used to assess the accuracy of the numerical method. The numerical results have
shown that this compacton exhibits
 true soliton behavior.
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\centerline{\bf REFERENCE}
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\item{1.} R. Rosenau, J. M. Hyman: Compactons: Solitons with finite wave
lengths, Phys. Rev. Lett., 70, No. 5, P. 564(1993)
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