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SOLUTIONS OF A DERIVATIVE NONLINEAR SCHRÖDINGER HIERARCHY AND ITS SIMILARITY REDUCTION

Published online by Cambridge University Press:  14 July 2005

SABURO KAKEI  and
TETSUYA KIKUCHI
SABURO KAKEI
Affiliation:
Department of Mathematics, Rikkyo University, Nishi-ikebukuro, Toshima-ku, Tokyo 171-8501, Japan e-mail: kakei@rkmath.rikkyo.ac.jp
TETSUYA KIKUCHI
Affiliation:
Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan e-mail: tkikuchi@math.tohoku.ac.jp
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Abstract

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The hierarchy structure of a derivative nonlinear Schrödinger equation is investigated in terms of the Sato-Segal-Wilson formulation. Special solutions are constructed as ratios of Wronski determinants. Relations to the Painlevé IV and the discrete Painlevé I are discussed by applying a similarity reduction.

Keywords

35Q5135Q5537K10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 47 , Issue A , June 2005 , pp. 99 - 107
Copyright
2005 Glasgow Mathematical Journal Trust