5,982 research outputs found
Integrable quasiclassical deformations of algebraic curves
No full text©IOP Publishing.
L Martinez Alonso wishes to thank the members of the Physics Department of Lecce University for their warm hospitality. This work was partially supported by DGCYT project BFM2002- 01607 and by the grant COFIN 2002 ‘Sintesi’.A general scheme for determining and studying integrable deformations of algebraic curves, based on the use of Lenard relations, is presented. The method is illustrated with the analysis of the hyperelliptic case. An associated multi-Hamiltonian hierarchy of systems of hydrodynamic type is characterized.DGCYTCOFINDepto. de Física TeóricaFac. de Ciencias FísicasTRUEpu
Nonlinear Dynamics on the Plane and Integrable Hierarchies of Infinitesimal Deformations
No full text©2002 by the Massachusetts Institute of Technology.
The authors are very grateful to the Isaac Newton Institute for Mathematical Sciences of Cambridge, where this work has been done and written, for the kind hospitality. They are also grateful to the organizers of the programme “Integrable Systems” for the support provided. L. Martínez Alonso wishes to thank the Fundacion Banco Bilbao Vizcaya Argentaria for supporting his stay at Cambridge University as a BBV visiting professor.A class of nonlinear problems on the plane, described by nonlinear inhomogeneous ∂¯-equations, is considered. It is shown that the corresponding dynamics, generated by deformations of inhomogeneous terms (sources), is described by Hamilton–Jacobi-type equations associated with hierarchies of dispersionless integrable systems. These hierarchies are constructed by applying the quasiclassical ∂¯-dressing method.Depto. de Física TeóricaFac. de Ciencias FísicasTRUEpu
Dispersionless scalar integrable hierarchies, Whitham hierarchies and quasiclasical D-bar-dressing method
No full textIntegrable deformations of algebraic curves
No full text©2005 Springer Science+Business Media, Inc.
One of the authors (L. M. A.) thanks the members of the Physics Department of Lecce University for their warm hospitality.
This work was supported in part by the DGCYT (Project No. BFM2002-01607), COFIN (Grant 2002 “Sintesi”), and the National Science Foundation (Grant No. DMS-0404931).We present a general scheme for determining and studying integrable deformations of algebraic curves, based on the use of Lenard relations. We emphasize the use of several types of dynamical variables: branches, power sums, and potentials.DGCYTCOFINNational Science FoundationDepto. de Física TeóricaFac. de Ciencias FísicasTRUEpu
D-bar-equations , integrable deformations of quasiconformal mappings and Whitham hierarchy
No full text©2001 Elsevier Science B.V. All rights reserved.
We would like to thank Prof. E. Medina for carrying out the computer calculation of the coefficients in the second example of Section 4. B.K. is supported in part by COFIN 2000 “Sintesi” and L.M.A. by proyecto PB98-0821.It is shown that the dispersionless scalar integrable hierarchies and, in general, the universal hitham hierarchy are nothing but classes of integrable deformations of quasiconformal mappings on the plane. Examples of deformations of quasiconformal mappings associated with explicit solutions of the dispersionless KP hierarchy are presented.COFINCICYTDepto. de Física TeóricaFac. de Ciencias FísicasTRUEpu
Singular sector of the KP hierarchy , D-bar operators of non-zero index and associated integrable systems
No full textHodograph solutions of the dispersionless coupled KdV hierarchies, critical points and Euler-Poisson-Darboux equation
No full textIt is shown that the hodograph solutions of the dispersionless coupled KdV hierarchies describe critical and degenerate critical points of a scalar function which obeys the Euler-Poisson-Darboux equation
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