On Gelfand–Dickey and Drinfeld–Sokolov Systems
نویسندگان
چکیده
We study the connections between Gelfand–Dickey (GD) systems and their modified counterparts, the Drinfeld–Sokolov (DS) systems in the case of general matrix–valued coefficients with entries in a commutative algebra over an arbitrary field. Our main results describe auto–Bäcklund transformations for the GD hierarchy based on Miura–type transformations associated with factorizations of n-th order linear differential expressions. Department of Mathematics, University of Missouri, Columbia, MO 65211, USA. E–Mail: [email protected] Department of Mathematical and Computing Sciences, University of Surrey, Guildford, Surrey GU2 5XH, England. E–Mail: [email protected] Institute for Theoretical Physics, Technical University of Graz, A–8010 Graz, Austria. Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich by an E. Schrödinger Fellowship and by Project No. P7425 Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA. E–Mail: [email protected]
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