Bilinear discrete Painleve-II and its particular solutions

J. Satsuma; K. Kajiwara; B. Grammaticos; J. Hietarinta; A. Ramani

doi:10.1088/0305-4470/28/12/025

Bilinear discrete Painleve-II and its particular solutions

J. Satsuma, K. Kajiwara, B. Grammaticos, J. Hietarinta, A. Ramani

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

Abstract

By analogy to the continuous Painleve-II equation, we present particular solutions of the discrete Painleve-II (d-P_II) equation. These solutions are of a rational and special function (Airy) type. Our analysis is based on the bilinear formalism that allows us to obtain the tau -function for d-P_II. Two different forms of bilinear d-P_II are obtained and we show that they can be related by a simple gauge transformation.

Original language	English
Article number	025
Pages (from-to)	3541-3548
Number of pages	8
Journal	Journal of Physics A: General Physics
Volume	28
Issue number	12
DOIs	https://doi.org/10.1088/0305-4470/28/12/025
Publication status	Published - 1995
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Physics and Astronomy(all)
Mathematical Physics

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10.1088/0305-4470/28/12/025

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AU - Satsuma, J.

AU - Kajiwara, K.

AU - Grammaticos, B.

AU - Hietarinta, J.

AU - Ramani, A.

PY - 1995

Y1 - 1995

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AB - By analogy to the continuous Painleve-II equation, we present particular solutions of the discrete Painleve-II (d-PII) equation. These solutions are of a rational and special function (Airy) type. Our analysis is based on the bilinear formalism that allows us to obtain the tau -function for d-PII. Two different forms of bilinear d-PII are obtained and we show that they can be related by a simple gauge transformation.

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Bilinear discrete Painleve-II and its particular solutions

Abstract

All Science Journal Classification (ASJC) codes

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