arXiv subjects
Publications and source records attributed to A. R. Aguirre.
In this paper we derive the type-II integrable defect for the N = 2 supersymmetric sinh-Gordon (sshG) model by using the fusing procedure. In particular, we show explicitly the conservation of the modified energy, momentum and supercharges.
A new super-Backlund transformation for the N=1 supersymmetric sinh-Gordon equation is constructed. Based on this construction we propose a type-II integrable defect for the supersymmetric sinh-Gordon model consistent with this new transformation through the Lagrangian formalism. Explicit expressions for the modified conserved energy, momentum and supercharges are also computed. In addition, we show for the model that the type-II defect can also been regarded as a pair of fused defects of a previously introduced type. The explicit derivation of the associated defect matrices is also presented as a necessary condition for the integrability of the model.
The Lax pair formalism is considered to discuss the integrability of the N=1 supersymmetric sinh-Gordon model with a defect. We derive associated defect matrix for the model and construct the generating functions of the modified conserved quantities. The corresponding defect contributions for the modified energy and momentum of the model are explicitly computed.
The introduction of type-II defects is discussed under the Lagrangian formalism and Lax representation for the N=1 super-Liouville model. We derive a new kind of super-Backlund transformation for the model and show explicitly the conservation of the modified energy and momentum, as well as supercharge.
We examine the N=1 super sinh-Gordon (SShG) model restricted into the half line through a reduction from the defect SShG model. The Bäcklund transformations are employed to generate one-, two- and three-soliton solutions as well as a class of breathers solution for this model. The parameters of such classical solutions are shown to satisfy some contraints in order to preserve both integrability and supersymmetry properties of the original bulk theory. Additionally, previous results are recovered when performing the purely bosonic limit.
We discuss the integrability of the Bosonic and Grassmannian massive Thirring models in the presence of defects through the inverse scattering approach. We present a general method to compute the generating functions of modified conserved quantities for any integrable field equation associated to the m x m spectral linear problem. We apply the method to derive in particular the defect contributions for the number of occupation, energy and momentum of the massive Thirring models.
The construction of type II Backlund transformation for the sine-Gordon and the Tzitzeica-Bullough-Dodd models are obtained from gauge transformation. An infinite number of conserved quantities are constructed from the defect matrices. This guarantees that the introduction of type II defects for these models does not spoil their integrability. In particular, modified energy and momentum are derived and compared with those presented in recent literature.
In this paper we discuss the Lax formulation of the Grassmanian and Bosonic Thirring models in the presence of jump defects. For the Grassmanian case, the defect is described by Bäcklund transformation which is responsible for preserving the integrability of the model. We then propose an extension of the Bäcklund transformation for the Bosonic Thirring model which is verified by some Bäcklund transitions like Vacuum-One soliton, One soliton - One soliton, One soliton - Two solitons and Two solitons - Two solitons. The Lax formulation within the space split by the defect leads to the integrability of Bosonic Thirring model.
The purpose of our work is to extend the formulation of classical affine Toda Models in the presence of jump defects to pure fermionic Thirring model. As a first attempt we construct the Lagrangian of the Grassmanian Thirring model with jump defect (of Backlund type) and present its conserved modified momentum and energy expressions giving a first indication of its integrability.