Abstract
We introduce a new discrete integrability criterion inspired from the recent findings of Ablowitz and collaborators. This criterion is based on the study of the growth of some characteristic of the solutions of a mapping, using Nevanlinna theory. Since the practical implementation of the latter does not always lead to a clear-cut answer, we complement the growth criterion by the singularity confinement property. This combination turns out to be particularly efficient. Its application allows us to recover the known forms of the discrete Painlevé equations and to show that no new ones may exist within a given parametrization.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
