ISSN:
1573-0530
Schlagwort(e):
33E30
;
39A10
;
58F07
;
58F08
;
discrete painlevé equations
;
Miura transformations
;
particular solutions
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
,
Physik
Notizen:
Abstract We derive the form of the Miura transformation of the discrete Pv equation and show that it is indeed an auto-Bäcklund transformation, i.e. it relates the discrete Pv to itself. Using this auto-Bäcklund, we obtain the Schlesinger transformations of discrete Pv which relate the solution for one set of the parameters of the equation to that of another set of neighbouring parameters. Finally, we obtain particular solutions of the discrete Pv (i.e. solutions that exist only for some specific values of the parameters). These solutions are of two types: solutions involving the confluent hypergeometric function (on codimension-one submanifold of parameters) and rational solutions (on codimension-two submanifold of parameters).
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF00398353
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