ar X iv : 0 90 6 . 01 31 v 1 [ nl in . S I ] 3 1 M ay 2 00 9 Nonvanishing boundary conditions and dark solitons in the NLS model

ar X iv : h ep - t h / 01 01 05 9 v 2 1 4 M ay 2 00 1

We consider the complex scalar field coupled to background NC U(1) YM and calculate the correlator of two gauge invariant composite operators. We show how the noncommutative gauge invariance is restored for higher correlators (though the Green's function itself is not invariant). It is interesting that the recently discovered noncommutative solitons appear in the calculation.

ar X iv : h ep - p h / 02 05 01 6 v 1 2 M ay 2 00 2 Scalar a 0 ( 980 ) meson in φ → π 0 ηγ decay

ar X iv : c on d - m at / 0 31 10 59 v 1 4 N ov 2 00 3 Dark Matter - Wave Solitons in Optical Lattices

We analyze the Floquet-Bloch matter-wave spectrum of Bose-Einstein condensates loaded into single-periodic optical lattices and double-periodic superlattices. In the framework of the Gross-Pitaevskii equation, we describe the structure and analyze the mobility properties of dark matter-wave solitons residing on the background of extended nonlinear Bloch-type states. We demonstrate that interact...

ar X iv : 0 90 3 . 31 52 v 1 [ nl in . S I ] 1 8 M ar 2 00 9 Symmetries and integrability of discrete equations defined on a black – white lattice

We study the deformations of the H equations, presented recently by Adler, Bobenko and Suris, which are naturally defined on a black-white lattice. For each one of these equations, two different three-leg forms are constructed, leading to two different discrete Toda type equations. Their multidimensional consistency leads to Bäcklund transformations relating different members of this class, as ...

ar X iv : 0 90 6 . 01 60 v 1 [ m at h . FA ] 3 1 M ay 2 00 9 OPERATOR MACHINES ON DIRECTED GRAPHS PETR

We show that if an infinite-dimensional Banach space X has a symmetric basis then there exists a bounded, linear operator R : X −→ X such that the set A = {x ∈ X : ||R(x)|| → ∞} is non-empty and nowhere dense in X . Moreover, if x ∈ X \ A then some subsequence of (R(x)) n=1 converges weakly to x. This answers in the negative a recent conjecture of Prǎjiturǎ. The result can be extended to any Ba...