Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2004-08-05
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Latex, 16 pages
Scientific paper
We investigate self-similar solutions of the extended discrete KP hierarchy. It is shown that corresponding ansatzes lead to purely discrete equations with dependence on some number of parameters together with equations governing deformations with respect to these parameters. Some examples are provided. In particular, it is shown that the well known discrete first Painleve equation (dPI) and its hierarchy arises as self-similar reduction of Volterra lattice hierarchy which in turn can be treated as a reduction of the extended discrete KP hierarchy. It is written down equations which naturally generalize dPI. It is shown that theses discrete systems describe B\"acklund transformations of Noumi-Yamada systems of type $A_{2(n-1)^{(1)}}$. We also consider Miura transformations relating different infinite- and finite-field integrable mappings. Simplest example of this kind of Miura transformations is given.
No associations
LandOfFree
Integrable Mappings Related to the Extended Discrete KP Hierarchy 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 Integrable Mappings Related to the Extended Discrete KP Hierarchy, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Integrable Mappings Related to the Extended Discrete KP Hierarchy will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-500971