RT Journal Article T1 Scaling self-similar formulation of the string equations of the hermitian one-matrix model A1 Mañas Baena, Manuel AB The string equation appearing in the double scaling limit of the Hermitian one–matrix model, which corresponds to a Galilean self–similar condition for the KdV hierarchy, is reformulated as a scaling self–similar condition for the Ur–KdV hierarchy. A non– scaling limit analysis of the one–matrix model has led to the complexified NLS hierarchy and a string equation. We show that this corresponds to the Galilean self– similarity condition for the AKNS hierarchy and also its equivalence to a scaling self– similar condition for the Heisenberg ferromagnet hierarchy. PB Elsevier Science BV SN 0370-2693 YR 1993 FD 1993-11-11 LK https://hdl.handle.net/20.500.14352/59706 UL https://hdl.handle.net/20.500.14352/59706 LA eng NO [1] M.Adler and J.Moser, Commun.Math.Phys. 61 (1978) 1. [2] E.Brezin and V.Kazakov, Phys.Lett. 236B (1990) 144; M.Douglas and M.Shenker, Nucl.Phys. B335 (1990) 685; D.Gross and A.Migdal, Phys.Rev.Lett. 64 (1990) 127. [3] L.Bonora and C.Xiong, Phys.Lett. 285B (1992) 191; Matrix models without scaling limit Int.J.Mod.Phys. A (1993) to appear. [4] S.Dalley, C.Johnson, and T.Morris, Nuc.Phys. B368 (1992) 625, 655; S.Dalley, preprint PUPT, 1290 (1991); C.Johnson, T.Morris, and Wätterstam, Phys.Lett. 291B (1992) 11; C.Johnson, T.Morris, and P.White, Phys.Lett. 292B (1992) 283; S.Dalley, C.Johnson, T.Morris, and A.Wättersman, Mod.Phys.Lett. A29 (1992) 2753; A.Wättersman, Phys.Lett. 263B (1991) 51. [5] L.Faddeev and L.Takhtajan, Hamiltonian Methods in the Theory of Solitons Springer Verlag (1987), Berlin. [6] A.Forsyth, Theory of Functions of Complex Variable Cambridge University Press (1893), Cambridge. [7] I.Gel’fand and L.Dickii, Russ.Math.Surv. 30 (1975) 67; Func.Anal.Appl. 13 (1979) 6. [8] F.Guil and M.Mañas, Phys.Lett. 153A (1991) 90. [9] F.Guil and M.Mañas, Self–similarity in the KdV hierarchy. Geometry of the string equations in Nonlinear Evolution Equations and Dynamical Systems’92 edited by V.Mahankov, O.Pashaev, and I.Puzynin, World Scientific (1992), Singapure; Strings equations for the KdV hierarchy and the Grassmannian J.Phys.A: Math. & Gen. (1993), to appear. [10] V.Kac and A.Schwarz, Phys.Lett. 257B (1991) 329. [11] I.Krichever and S.Novikov, Russ.Math.Surv. 35 (1980) 53. [12] H.La, Mod.Phys.Lett.A 6 (1991) 573; Commun.Math.Phys. 140 (1991) 569. [13] I.McIntosh, Proc.Roy.Soc. Edinburgh 115A (1990) 367. [14] W.Magnus, F.Oberhettinger, and R.Soni, Formulas and Theorems for the Special Functions of Mathematical Physics Springer Verlag (1966), Berlin. [15] M.Mañas and P.Guha, String equations for the unitary matrix model and the periodic flag manifold (1993) to appear. [16] S.Svinolupov and V.Sokolov, Func.Anal.Appl. 16 (1983) 317; S.Svinolupov, V.Sokolov, and R.Yamilov, Sov.Math.Dokl. 28 (1983) 165. [17] G.Wilson, Phys.Lett. 132A (1989) 445. [18] E.Witten, Surv.Diff.Geom. 1 (1991) 243; M.Kontsevich, Commun.Math.Phys. 147 (1992) 1. NO ©Elsevier Science BV. DS Docta Complutense RD 20 may 2024