Continuous limit of the difference second Painleve equation and its asymptotic solutions

Shun Shimomura

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Continuous limit of the difference second Painleve equation and its asymptotic solutions

机译：差分第二Painleve方程的连续极限及其渐近解

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The discrete second Painleve equation dP_Ⅱ is mapped to the second Painleve 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 dPn-Furthermore we show the existence of families of solutions having sequential limits to truncated solutions of P_Ⅱ.

机译：离散的第二Painleve方程dP_Ⅱ通过其连续极限映射到第二Painleve方程P_Ⅱ，然后，如Kajiwara等人所示，dP_Ⅱ的有理解也降为P_Ⅱ的有理解。本文以dP_Ⅱ为差方程，我们给出了一个渐近解，在该连续极限下，它可以简化为P_Ⅱ的三截式解。在一种特殊情况下，我们的解对应于dPn的一个有理数，此外，我们证明了解的族存在，这些族对P_Ⅱ的截断解具有顺序限制。

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来源
《Journal of the Mathematical Society of Japan》 |2012年第3期|p.733-781|共49页
作者
Shun Shimomura;
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作者单位

Department of Mathematics Keio University 3-14-1, Hiyoshi, Kohoku-ku Yokohama 223-8522 Japan;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
difference second painleve equation; second painleve equation; continuous limit; asymptotic solution;

机译：差分第二痛苦方程;第二痛苦方程;连续极限渐近解;

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Continuous limit of the difference second Painleve equation and its asymptotic solutions

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