Abstract
The discrete second Painlevé equation dP II is mapped to the second Painlevé equation P II by its continuous limit, and then, as shown by Kajiwara et al., a rational solution of dP II also reduces to that of P II. In this paper, regarding dP II as a difference equation, we present a certain asymptotic solution that reduces to a triply-truncated solution of P II in this continuous limit. In a special case our solution corresponds to a rational one of dP II. Furthermore we show the existence of families of solutions having sequential limits to truncated solutions of P II.
| Original language | English |
|---|---|
| Pages (from-to) | 733-781 |
| Number of pages | 49 |
| Journal | Journal of the Mathematical Society of Japan |
| Volume | 64 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2012 |
Keywords
- Asymptotic solution
- Continuous limit
- Difference second Painlevé equation
- Second Painlevé equation
ASJC Scopus subject areas
- Mathematics(all)