T-Duality in 2-D Integrable Models

The non-conformal analog of abelian T-duality transformations relating pairs of axial and vector integrable models from the non abelian affine Toda family is constructed and studied in detail.Comment: 14 pages, Latex, v.2 misprints corrected, reference added, to appear in J. Phys.

Type-II super-Backlund transformation and integrable defects for the N=1 super sinh-Gordon model

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.Comment: Latex 31 pages. Version accepted for publicatio

Why are the Properties of Polycyclic Hydrocarbons Additive over Conjugation Circuits?

Properties as different as resonance energies and magnetic ring-currents are investigated and a non-empirical system of increments is proposed. It is shown that the :n:-electron properties of · conjugated, polycyclic hydrocarbons are additive over all conjugation circuits that can be identified in the molecule. The contribution from each individual conjugation circuit is calculated non-empirically on a simple, free-electron model for the associated annulene. Within a special form of the resonance theory, it is shown that all conjugation circuits should contribute with equal weight, and not only the »independent circuits« as proposed earlier by Randie or certain lower circuits as postulated by Herndon. Contributions from higher circuits turn out quite naturally, however, to be small. Results for a wide variety of polycyclic hydrocarbons, alternant and non-alternant, are presented. Both for resonance energies and for magnetically-induced ring-currents, very satisfactory agreement with conventional calculations has been obtained

Why are the Properties of Polycyclic Hydrocarbons Additive over Conjugation Circuits?

Properties as different as resonance energies and magnetic ring-currents are investigated and a non-empirical system of increments is proposed. It is shown that the :n:-electron properties of · conjugated, polycyclic hydrocarbons are additive over all conjugation circuits that can be identified in the molecule. The contribution from each individual conjugation circuit is calculated non-empirically on a simple, free-electron model for the associated annulene. Within a special form of the resonance theory, it is shown that all conjugation circuits should contribute with equal weight, and not only the »independent circuits« as proposed earlier by Randie or certain lower circuits as postulated by Herndon. Contributions from higher circuits turn out quite naturally, however, to be small. Results for a wide variety of polycyclic hydrocarbons, alternant and non-alternant, are presented. Both for resonance energies and for magnetically-induced ring-currents, very satisfactory agreement with conventional calculations has been obtained

N=1 super sinh-Gordon model with defects revisited

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.Comment: Latex 26 page

Defects in the supersymmetric mKdV hierarchy via Backlund transformations

The integrability of the ${\cal N}=1$ supersymmetric modified Korteweg de-Vries (smKdV) hierarchy in the presence of defects is investigated through the construction of its super B\"acklund transformation. The construction of such transformation is performed by using essentially two methods: the B\"acklund-defect matrix approach and the superfield approach. Firstly, we employ the defect matrix associated to the hierarchy which turns out to be the same for the supersymmetric sinh-Gordon (sshG) model. The method is general for all flows and as an example we derive explicitly the B\"acklund equations in components for the first few flows of the hierarchy, namely $t_3$ and $t_5$. Secondly, the supersymmetric extension of the B\"acklund transformation in the superspace formalism is constructed for those flows. Finally, this super B\"acklund transformation is employed to introduce type I defects for the supersymmetric mKdV hierarchy. Further integrability aspects by considering modified conserved quantities are derived from the defect matrix.Comment: 40 pages. Some comments and references added. Version accepted for publication in JHE

Vertex Operators and Soliton Solutions of Affine Toda Model with U(2) Symmetry

The symmetry structure of non-abelian affine Toda model based on the coset $SL(3)/SL(2)\otimes U(1)$ is studied. It is shown that the model possess non-abelian Noether symmetry closing into a q-deformed $SL(2)\otimes U(1)$ algebra. Specific two vertex soliton solutions are constructed.Comment: 17 pages, latex, misprints corrected, version to appear in J.Phys