Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 9 (2013), 073, 12 pages      arXiv:1309.4949      http://dx.doi.org/10.3842/SIGMA.2013.073

Direct Connection between the RII Chain and the Nonautonomous Discrete Modified KdV Lattice

Kazuki Maeda and Satoshi Tsujimoto
Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan

Received September 20, 2013, in final form November 22, 2013; Published online November 26, 2013

Abstract
The spectral transformation technique for symmetric RII polynomials is developed. Use of this technique reveals that the nonautonomous discrete modified KdV (nd-mKdV) lattice is directly connected with the RII chain. Hankel determinant solutions to the semi-infinite nd-mKdV lattice are also presented.

Key words: orthogonal polynomials; spectral transformation; RII chain; nonautonomous discrete modified KdV lattice.

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