The short-range delta-nucleon interaction

Ferreira, E.; Andrade, Sarah C.B.; Dosch, H. G.

doi:10.1088/0305-4616/13/4/002

Cited by 20 publications

(28 citation statements)

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“…Another important restriction in the results of [16] is that they do not include the important class of integrable equations known as generalized Toda equations; e.g., they do not explain the change of variables (1.2). Nevertheless, inspired by the results of [16], a definition for the tau-functions of the Toda equations has been proposed in [17].…”

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confidence: 99%

“…The aim of this paper is to generalize the results of [16] and [17] in order to clarify the definition and relevance of tau-functions for a large class of integrable equations including both the integrable hierarchies of [15] and the non-abelian generalizations of the Toda equation. In our approach, the central role will be played by the dressing transformations in the manner described by Wilson [10,11].…”

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confidence: 99%

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

Ferreira

Miramontes

Sánchez-Guillén

1997

Journal of Mathematical Physics

109

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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.

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confidence: 99%

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confidence: 99%

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

Ferreira

Miramontes

Sánchez-Guillén

1997

Journal of Mathematical Physics

109

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“…Moreover, Eq. (15) is the analogue of the, so called, solitonic specialization of the Leznov-Saveliev solution proposed in [6][7][8][9] for the affine (abelian and non-abelian) Toda theories. Consider now the common eigenvectors of the adjoint action of the ε N 's that specify the vacuum solution (6).…”

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confidence: 99%

“…Consequently, the solutions obtained through the group of dressing transformations can also be understood in terms of the solutions of the larger hierarchy, which implies certain relations among them. (see section 4 of [8] for more details).…”

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confidence: 99%

The structures underlying soliton solutions in integrable hierarchies

Ferreira¹

1997

AIP Conference Proceedings

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We point out that a common feature of integrable hierarchies presenting soliton solutions is the existence of some special ``vacuum solutions'' such that the Lax operators evaluated on them, lie in some abelian subalgebra of the associated Kac-Moody algebra. The soliton solutions are constructed out of those ``vacuum solitons'' by the dressing transformation procedure.Comment: Talk given at the I Latin American Symposium on High Energy Physics, I SILAFAE, Merida, Mexico, November/96, 5 pages, LaTeX, needs aipproc.tex, aipproc.sty, aipproc.cls, available from ftp://ftp.aip.org/ems/tex/macros/proceedings/6x9

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“…For example, it has long been noted that there exist significant discrepancies between theory and experiment in the cross sections and iT\\ above 180 MeV. Ferreira et al 17 have attempted to account for these by introducing intermediate short-range A-7V interactions. Using the amplitude calculations of Garcilazo and three additional partial waves from these channels they were able to accurately describe all the cross sections and iT\\ data.…”

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confidence: 99%