arXiv subjects

Hikaru Igarashi

Publications and source records attributed to Hikaru Igarashi.

2 recordsLinked to original sources

arXiv2018

On two-parameter solutions of simultaneous ultradiscrete Painleve II equation with parity variables

We introduce a simultaneous ultradiscrete Painleve II equation with parity variables, which is shown to be more suitable for studying two-parameter solutions than the single second-order ultradiscrete Painleve II equation with parity variables. We investigate several types of two-parameter solutions and the solutions which are related with the ultradiscrete limit of determinant type solutions of q-Painleve II equation.

math.CA↗

arXiv2015

New Airy-type solutions of the ultradiscrete Painleve II equation with parity variables

The q-difference Painleve II equation admits special solutions written in terms of determinant whose entries are the general solution of the q-Airy equation. An ultradiscrete limit of the special solutions is studied by the procedure of ultradiscretization with parity varialbes. Then we obtain new Airy-type solutions of the ultradiscrete Painleve II equation with parity variables, and the solutions have richer structure than the known solutions.

math.CA↗