On some algebraic examples of Frobenius manifolds

We construct some explicit quasihomogeneous algebraic solutions to the associativity (WDVV) equations by using analytical methods of the finite gap integration theory. These solutions are expanded in the uniform way to non-semisimple Frobenius manifolds.Comment: 14 page

Vanishing Meissner effect as a hallmark of in-plane FFLO instability in superconductor - ferromagnet layered systems

We demonstrate that in a wide class of multilayered superconductor - ferromagnet structures (e.g., S/F, S/F/N and S/F/F') the vanishing Meissner effect signals the appearance of the in-plane Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) modulated superconducting phase. In contrast to the bulk superconductors the FFLO instability in these systems can emerge at temperatures close to the critical one and is effectively controlled by the S layer thickness and the angle between magnetization vectors in the F/F' bilayers. The predicted FFLO state reveals through the critical temperature oscillations vs the perpendicular magnetic field component.Comment: 5 pages, 5 figure

Stabilization of dipole solitons in nonlocal nonlinear media

We address the stabilization of dipole solitons in nonlocal nonlinear materials by two different approaches. First, we study the properties of such solitons in thermal nonlinear media, where the refractive index landscapes induced by laser beams strongly depend on the boundary conditions and on the sample geometry. We show how the sample geometry impacts the stability of higher-order solitons in thermal nonlinear media and reveal that dipole solitons can be made dynami-cally stable in rectangular geometries in contrast to their counterparts in thermal samples with square cross-section. Second, we discuss the impact of the saturation of the nonlocal nonlinear response on the properties of multipole solitons. We find that the saturable response also stabi-lizes dipole solitons even in symmetric geometries, provided that the input power exceeds a criti-cal value.Comment: 29 pages, 8 figures, to appear in Phys. Rev.

Stabilization of higher-order vortices and multi-hump solitons in media with synthetic nonlocal nonlinearities

We address the evolution of higher-order excited states, such as vortex and multi-hump solitons, in nonlocal media with synthetic, competing focusing and defocusing nonlinearities with different nonlocal transverse scales. We reveal that introduction of suitable competing effects makes possible the stabilization of vortex solitons with topological charge m>2, as well as one-dimensional multi-hump solitons with number of humps p>4, all of which are highly unstable in natural nonlocal materials with focusing nonlinearities.Comment: 14 pages, 5 figures, to appear in Physical Review