On the Lax pairs of the sixth Painleve' equation

Details On the Lax pairs of the sixth Painleve' equation On the Lax pairs of the sixth Painleve' equation

2007-01-24

arxiv.org/abs/nlin/0701049v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

6 pages, no figure, se'minaire franco-Japonais, Kyoto, 15-20 May 2006

Scientific paper

The dependence of the sixth equation of Painleve' on its four parameters $(2 \alpha,-2 \beta,2 \gamma,1-2 \delta) =(\theta_{\infty}^2,\theta_{0}^2,\theta_{1}^2,\theta_{x}^2)$ is holomorphic, therefore one expects all its Lax pairs to display such a dependence. This is indeed the case of the second order scalar ``Lax'' pair of Fuchs, but the second order matrix Lax pair of Jimbo and Miwa presents a meromorphic dependence on $\theta_\infty$ (and a holomorphic dependence on the three other $\theta_j$). We analyze the reason for this feature and make suggestions to suppress it.

Affiliated with

Also associated with

No associations

Rating

On the Lax pairs of the sixth Painleve' equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Lax pairs of the sixth Painleve' equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Lax pairs of the sixth Painleve' equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-603975