Electron. J. Diff. Eqns., Vol. 2008(2008), No. 86, pp. 1-11.

Travelling wave solutions for the Painleve-integrable coupled KdV equations

Jibin Li, Xiao-Biao Lin

We study the travelling wave solutions for a system of coupled KdV equations derived by Lou et al [11]. In that paper, they found 5 types of Painleve integrable systems for the coupled KdV system. We show that each of them can be reduced to a partially or completely uncoupled system, through which the dynamical behavior of travelling wave solutions can be determined. In some parameter regions, exact formulas for periodic and solitary waves can be obtained while in other cases, bounded travelling wave solution are discussed.

Submitted February 15, 2008. Published June 10, 2008.
Math Subject Classifications: 34A05, 34B99, 34C20, 34C25, 34C37, 35B99, 35C15.
Key Words: Coupled KdV equations; Paileve integrable systems; bounded solutions; solitary waves; periodic waves.

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Jibin Li
Department of Mathematics
Kunming University of Science and Technology
Kunming, Yunnan, 650093, China
email: jibinli@gmail.com
Xiao-Biao Lin
Department of Mathematics, North Carolina State University
Raleigh, NC 27695, USA
email: xblin@math.ncsu.edu

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