Tau-functions and dressing transformations for zero-curvature affine integrable equations


Autoria(s): Ferreira, Luiz A.; Miramontes, J. Luis; Guillén, Joaquín Sánchez
Contribuinte(s)

Universidade Estadual Paulista (UNESP)

Data(s)

27/05/2014

27/05/2014

01/02/1997

Resumo

The solutions of a large class of hierarchies of zero-curvature equations that includes Toda- and KdV-type hierarchies are investigated. All these hierarchies are constructed from affine (twisted or untwisted) Kac-Moody algebras g. Their common feature is that they have some special vacuum solutions corresponding to Lax operators lying in some Abelian (up to the central term) subalgebra of g; in some interesting cases such subalgebras are of the Heisenberg type. Using the dressing transformation method, the solutions in the orbit of those vacuum solutions are constructed in a uniform way. Then, the generalized tau-functions for those hierarchies are defined as an alternative set of variables corresponding to certain matrix elements evaluated in the integrable highest-weight representations of g. Such definition of tau-functions applies for any level of the representation, and it is independent of its realization (vertex operator or not). The particular important cases of generalized mKdV and KdV hierarchies as well as the Abelian and non-Abelian affine Toda theories are discussed in detail. © 1997 American Institute of Physics.

Formato

882-901

Identificador

http://dx.doi.org/10.1063/1.531895

Journal of Mathematical Physics, v. 38, n. 2, p. 882-901, 1997.

0022-2488

http://hdl.handle.net/11449/65033

10.1063/1.531895

WOS:A1997WF65500024

2-s2.0-0031540337

2-s2.0-0031540337.pdf

Idioma(s)

eng

Relação

Journal of Mathematical Physics

Direitos

closedAccess

Tipo

info:eu-repo/semantics/article