RT Journal Article T1 String equations in Whitham hierarchies: τ-functions and Virasoro constraints A1 Martínez Alonso, Luis A1 Medina Reus, Elena A1 Mañas Baena, Manuel AB A scheme for solving Whitham hierarchies satisfying a special class of string equations is presented. The τ-functions of the corresponding solutions is obtained and the differential expressions of the underlying Virasoro constraints are characterized. Illustrative examples of exact solutions of Whitham hierarchies are derived and applications to conformal maps dynamics are indicated. PB American Institute of Physics SN 0022-2488 YR 2006 FD 2006-08 LK https://hdl.handle.net/20.500.14352/51530 UL https://hdl.handle.net/20.500.14352/51530 LA eng NO 1 B. A. Kuperschmidt and Yu. I. Manin, Funct. Anal. Appl. 11, 31 1977; Funct. Anal. Appl. 17, 25 1978. 2 V. E. Zakharov, Funkc. Anal. Priloz. 14, 89 1980; Physica D 3, 193–202 1981. 3 Singular Limits of Dispersive Waves, edited by N. M. Ercolani et al., Nato Advanced Science Institute Series B Physics Vol. 320 Plenum, New York, 1994. 4 I. M. Krichever, Funct. Anal. Appl. 22, 200 1989. 5 I. M. Krichever, Commun. Pure Appl. Math. 47, 437 1992. 6 S. Aoyama and Y. Kodama, Commun. Math. Phys. 182, 185 1996. 7 Y. Gibbons and S. P. Tsarev, Phys. Lett. A 258, 263 1999. 8 B. Konopelchenko, L. Martínez Alonso, and O. Ragnisco, J. Phys. A 34, 10209 2001. 9 B. Konopelchenko and L. Martínez Alonso, Phys. Lett. A 286, 161 2001. 10P. W. Wiegmann and P. B. Zabrodin, Commun. Math. Phys. 213, 523 2000. 11M. Mineev-Weinstein, P. Wiegmann, and A. Zabrodin, Phys. Rev. Lett. 84, 5106 2000. 12A. Boyarsky, A. Marsahakov, O. Ruchaysky, P. Wiegmann, and A. Zabrodin, Phys. Lett. B 515, 483 2001. 13O. Agam, E. Bettelheim, P. Wiegmann, and A. Zabrodin, Phys. Rev. Lett. 88, 236801 2002. 14 I. Krichever, M. Mineev-Weinstein, P. Wiegmann, and A. Zabrodin, Physica D 198, 1 2004. 15A. Zabrodin, Teor. Mat. Fiz. 142, 197 2005. 16R. Teodorescu, E. Bettelheim, O. Agam, A. Zabrodin, and P. Wiegmann, Nucl. Phys. B 700, 521 2004; 704, 407 2005. 17V. Kazakov and A. Marsahakov, J. Phys. A 36, 3107 2003. 18K. Takasaki, Commun. Math. Phys. 170, 101 1995. 19K. Takasaki and T. Takebe, Lett. Math. Phys. 23, 205 1991. 20K. Takasaki and T. Takebe, Int. J. Mod. Phys. A 7, 889 1992. 21K. Takasaki and T. Takebe, Lett. Math. Phys. 28, 165 1993. 22K. Takasaki and T. Takebe, Rev. Math. Phys. 7, 743 1995. 23L. Martínez Alonso and M. Mañas, J. Math. Phys. 44, 3294 2003. 24L. Martínez Alonso and E. Medina, J. Phys. A 37, 12005 2004. 25L. Martínez Alonso and E. Medina, Phys. Lett. B 610, 227 2005. 26M. Mañas, E. Medina and L. Martínez Alonso, J. Phys. A 39, 2349 2006. 27P. Henrici, Applied and Computational Complex Analysis, Vol. 3 Wiley, New York, 1993. NO ©2006 American Institute of Physics.Partial economical supports from the Spanish DGCYT Program No. FIS2005-00319 and from the European Science Foundation Program No. MISGAM are acknowledged. NO DGCYT, Spain NO European Science Foundation Program DS Docta Complutense RD 30 abr 2024