Locality of symmetries generated by nonhereditary, inhomogeneous, and time-dependent recursion operators: a new application for formal symmetries

Using the methods of the theory of formal symmetries, we obtain new easily verifiable sufficient conditions for a recursion operator to produce a hierarchy of local generalized symmetries. An important advantage of our approach is that under certain mild assumptions it allows to bypass the cumbersome check of hereditariness of the recursion operator in question, what is particularly useful for the study of symmetries of newly discovered integrable systems. What is more, unlike the earlier work, the homogeneity of recursion operators and symmetries under a scaling is not assumed as well. An example of nonhereditary recursion operator generating a hierarchy of local symmetries is presented.Comment: 11 pages, LaTeX 2e, submitted to Acta Appl. Mat

Solitons in a hard-core bosonic system: Gross-Pitaevskii type and beyond

A unified formulation that obtains solitary waves for various background densities in the Bose-Einstein condensate of a system of hard-core bosons with nearest neighbor attractive interactions is presented. In general, two species of solitons appear: A nonpersistent (NP) type that fully delocalizes at its maximum speed, and a persistent (P) type that survives even at its maximum speed, and transforms into a periodic train of solitons above this speed. When the background condensate density is nonzero, both species coexist, the soliton is associated with a constant intrinsic frequency, and its maximum speed is the speed of sound. In contrast, when the background condensate density is zero, the system has neither a fixed frequency, nor a speed of sound. Here, the maximum soliton speed depends on the frequency, which can be tuned to lead to a cross-over between the NP-type and the P-type at a certain critical frequency, determined by the energy parameters of the system. We provide a single functional form for the soliton profile, from which diverse characteristics for various background densities can be obtained. Using the mapping to spin systems enables us to characterize the corresponding class of magnetic solitons in Heisenberg spin chains with different types of anisotropy, in a unified fashion