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Solution of Baxter equation for the $q$-Toda and Toda$_2$ chains by NLIE

Published 5 Apr 2018 in math-ph, math.MP, and nlin.SI | (1804.01749v3)

Abstract: We construct a basis of solutions of the scalar $\boldsymbol{ \texttt{t} }- \boldsymbol{ \texttt{Q} }$ equation describing the spectrum of the $q$-Toda and Toda$_2$ chains by using auxiliary non-linear integral equations. Our construction allows us to provide quantisation conditions for the spectra of these models in the form of thermodynamic Bethe Ansatz-like equations.

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