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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 k z i ( λ ) = k + 1 . The problem...

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