arXiv subjects

G. Cuba

Publications and source records attributed to G. Cuba.

3 recordsLinked to original sources

arXiv1999

Surfaces of Constant negative Scalar Curvature and the Correpondence between the Liouvulle and the sine-Gordon Equations

By studying the {\it internal} Riemannian geometry of the surfaces of constant negative scalar curvature, we obtain a natural map between the Liouville, and the sine-Gordon equations. First, considering isometric immersions into the Lobachevskian plane, we obtain an uniform expression for the general (locally defined) solution of both the equations. Second, we prove that there is a Lie-Bäcklund transformation interpolating between Liouville and sine-Gordon. Third, we use isometric immersions into the Lobachevskian plane to describe sine-Gordon N-solitons explicitly.

solv-int↗

arXiv1997

Vertex Operator Representation of the Soliton Tau Functions in the $A_n^{(1)}$ Toda Models by Dressing Transformations

We study the relation between the group-algebraic approach and the dressing symmetry one to the soliton solutions of the $A_n^{(1)}$ Toda field theory in 1+1 dimensions. Originally solitons in the affine Toda models has been found by Olive, Turok and Underwood. Single solitons are created by exponentials of elements which ad-diagonalize the principal Heisenberg subalgebra. Alternatively Babelon and Bernard exploited the dressing symmetry to reproduce the known expressions for the fundamental tau functions in the sine-Gordon model. In this paper we show the equivalence between these two methods to construct solitons in the $A_n^{(n)}$ Toda models.

hep-th↗

arXiv1996

A Note on the Symplectic Structure on the Dressing Group in the sinh--Gordon Model

We analyze the symplectic structure on the dressing group in the \shG\, model by calculating explicitly the Poisson bracket $\{g\x g\}$ where $g$ is the \dg\, element which creates a generic one soliton solution from the vacuum. Our result is that this bracket does not coincide with the Semenov--Tian--Shansky one. The last induces a Lie--Poisson structure on the \dg . To get the bracket obtained by us from the Semenov--Tian--Shansky bracket we apply the formalism of the constrained Hamiltonian systems. The constraints on the \dg\, appear since the element which generates one solitons from the vacuum has a specific form.

hep-th↗