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

Abstract

We construct a basis of solutions of the scalar $\text{t}-\text{Q}$ 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.

37 pages,1 figure, V3 minor corrections

References in corpus (4)

• Quantization condition from exact WKB for difference equations
• Spectral equations for the modular oscillator
• Baxter operator and Baxter equation for $q$-Toda and Toda${}_2$ chains
• The Toda${}_2$ chain

Cited by in corpus (2)

• On $b$-Whittaker functions
• Exact quantization conditions for the elliptic Ruijsenaars-Schneider model