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Generalized Gaudin models and Riccatians

Aleksander Ushveridze — 1996

Banach Center Publications

The systems of differential equations whose solutions exactly coincide with Bethe ansatz solutions for generalized Gaudin models are constructed. These equations are called the generalized spectral $(^{1})$ Riccati equations, because the simplest equation of this class has a standard Riccatian form. The general form of these equations is $R_{n_{i}} [z_{1} (λ), . . ., z_{r} (λ)] = c_{n_{i}} (λ)$ , i=1,..., r, where $R_{n_{i}}$ denote some homogeneous polynomials of degrees $n_{i}$ constructed from functional variables $z_{i} (λ)$ and their derivatives. It is assumed that $d e g \partial^{k} z_{i} (λ) = k + 1$ . The problem...

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