A Class of Special Solutions for the Ultradiscrete Painlevé II Equation
Abstract
A class of special solutions are constructed in an intuitive way for the ultradiscrete analog of q-Painlevé II (q-PII) equation. The solutions are classified into four groups depending on the function-type and the system parameter.
- Publication:
-
SIGMA
- Pub Date:
- July 2011
- DOI:
- 10.3842/SIGMA.2011.074
- arXiv:
- arXiv:1107.4416
- Bibcode:
- 2011SIGMA...7..074I
- Keywords:
-
- ultradiscretization;
- Painlevé equation;
- Airy equation;
- q-difference equation;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Mathematics - Classical Analysis and ODEs
- E-Print:
- SIGMA 7 (2011), 074, 9 pages