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.
- Asymptotic solution
- Continuous limit
- Difference second Painlevé equation
- Second Painlevé equation
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