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

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

Cited literature [9 references]

https://hal-cea.archives-ouvertes.fr/cea-01787571
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Submitted on : Monday, May 7, 2018 - 4:19:57 PM
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1804.01749.pdf
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### Citation

O. Babelon, K. Kozlowski, V. Pasquier. Solution of Baxter equation for the $q$-Toda and Toda$_2$ chains by NLIE. SciPost Phys., 2018, 5 (4), pp.035. ⟨10.21468/SciPostPhys.5.4.035⟩. ⟨cea-01787571⟩

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