Toda-Darboux maps and vertex operators

M. Adler; P. van Moerbeke

Toda-Darboux maps and vertex operators

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arxiv solv-int/9712016 v1 pith:PRFSEUCD submitted 1997-12-19 solv-int nlin.SI

M. Adler , P. van Moerbeke This is my paper · ORCID

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keywords toda-darbouxgivenoperatorstransformsvertexaccordingcertaindarboux

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abstract

The purpose of this paper is to study Toda-Darboux transforms, i.e., Darboux transforms for operators L(t) flowing according to the Toda lattice. Each element of the null-space $L(t)-z$ specifies a factorization for all t and thus a Toda-Darboux transform on $L(t)$. The Toda-Darboux map induces a transformation on the tau-vectors, given by a certain vertex operator, and on eigenfunctions, given by a Wronskian. .

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