In a previous letter [Velarde et al., 2005] a new form of electric conduction mediated by solitons was shown to be possible in an anharmonic Toda lattice. In the presence of an external electric field this current can be much higher than the Drude-Ohm linear current and, as the field is lowered, the current achieves a finite, constant, field-independent value. The model studied therein is stric...

In this paper we prove that the periodic Toda lattice admits globally defined Birkhoff coordinates.

We describe two ways to define higher order Toda brackets in a pointed simplicial model category $${\mathcal {D}}$$ : one is recursive definition using categorical constructions, and the second uses associated enrichment. show that these definitions agree, by providing third, diagrammatic, description of bracket, explain how it serves as obstruction rectifying certain homotopy-commutative diagr...

String equations of the p-th generalized Kontsevich model and the compactified c = 1 string theory are re-examined in the language of the Toda lattice hierarchy. As opposed to a hypothesis postulated in the literature, the generalized Kontsevich model at p = −1 does not coincide with the c = 1 string theory at self-dual radius. A broader family of solutions of the Toda lattice hierarchy includi...