Construction of a Lax Pair for the E ( 1 ) 6 q - Painlevé System
نویسندگان
چکیده
We construct a Lax pair for the E (1) 6 q-Painlevé system from first principles by employing the general theory of semi-classical orthogonal polynomial systems characterised by divided-difference operators on discrete, quadratic lattices [arXiv:1204.2328]. Our study treats one special case of such lattices – the q-linear lattice – through a natural generalisation of the big q-Jacobi weight. As a by-product of our construction we derive the coupled firstorder q-difference equations for the E (1) 6 q-Painlevé system, thus verifying our identification. Finally we establish the correspondences of our result with the Lax pairs given earlier and separately by Sakai and Yamada, through explicit transformations.
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