RT Journal Article T1 Quasiconformal mappings and solutions of the dispersionless KP hierarchy A1 Konopelchenko, Boris A1 Martínez Alonso, Luis A1 Medina Reus, Elena AB A ∂¯formalism for studying dispersionless integrable hierarchies is applied to the dispersionless KP (dKP) hierarchy. We relate this formalism to the theory of quasiconformal mappings on the plane and present some classes of explicit solutions of the dKP hierarch. PB Springer SN 0040-5779 YR 2002 FD 2002-11 LK https://hdl.handle.net/20.500.14352/59823 UL https://hdl.handle.net/20.500.14352/59823 LA eng NO 1. V. E. Zakharov, Funct. Anal. Appl., 14, 89–98 (1980); Phys. D, 3, 193–202 (1981); P. D. Lax and C. D. Levermore, Comm. Pure Appl. Math., 36, 253–290, 571–593, 809–830 (1983). 2. Y. Kodama, Phys. Lett. A, 129, 223–226 (1988); 147, 477–482 (1990); I. M. Krichever, Funct. Anal. Appl., 22, 200–213 (1988); Comm. Pure Appl. Math., 47, 437–475 (1994). 3. B. A. Dubrovin and S. P. Novikov, Russ. Math. Surveys, 44, 35–124(1989). 4. K. Takasaki and T. Takebe, Internat. J. Mod. Phys. A, Suppl. 1B, 7, 889–922 (1992); Rev. Math. Phys., 7, 743– 818 (1995). 5. N. M. Ercolani et al., eds., Singular Limits of Dispersive Waves (Nato Adv. Sci. Inst. Ser. B Phys., Vol. 320), Plenum, New York (1994). 6. I. M. Krichever, Comm. Math. Phys., 143, 415–429 (1992). 7. B. A. Dubrovin, Comm. Math. Phys., 145, 195–203 (1992); B. A. Dubrovin and Y. Zhang, Comm. Math. Phys., 198, 311–361 (1998); “Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov– Witten invariants,” math.DG/0108160 (2001) 8. M. Dunaiski, L. J. Mason, and P. Tod, J. Geom. Phys., 37, 63–93 (2001). 9. J. Gibbons and S. P. Tsarev, Phys. Lett. A, 258, 263-271 (1999); P. B. Wiegmann and A. Zabrodin, Comm. Math. Phys., 213, 523–538 (2000). 10. B. Konopelchenko, L. Martínez Alonso, and O. Ragnisco, J. Phys. A, 34, 10209–10217 (2001). 11. B. Konopelchenko and L. Mart´ınez Alonso, Phys. Lett. A, 286, 161–166 (2001). 12. I. N. Vekua, Generalized Analytic Functions [in Russian] (2nd ed.), Nauka, Moscow (1988); English transl., Pergamon, Oxford (1962). 13. L. V. Ahlfors, Lectures on Quasi-Conformal Mappings, Van Nostrand, Princeton (1966). 14. O. Lehto, Univalent Functions and Teichmüller Spaces, Springer, Berlin (1987). 15. O. Lehto and K. I. Virtanen, Quasiconformal Mappings in the Plane, Springer, Berlin (1973). 16. B. Bojarski, Symp. Math., 18, 485–499 (1976); T. Iwaniec, Symp. Math., 18, 501–517 (1976). NO ©2002 Plenum Publishing Corporation.International Conference on Nonlinear Evolution Equations and Dynamical Systems. (15. 2001. Cambridge, Inglaterrad).One of the authors (B. K.) is grateful to the organizers of the program “Integrable Systems” for the support and was also supported in part by the COFIN 2000 “Sintesi.” The stay of L. M. A. at Cambridge University as a BBV visiting professor was supported by the Fundaci´on Banco Bilbao Vizcaya Argentaria. E. M. was supported in part by the CICYT (Project No. PB98-0821). NO COFIN NO Fundación Banco Bilbao Vizcaya Argentaria NO CICYT DS Docta Complutense RD 16 may 2024