In contrast to an infinite degree of nonlocality, we demonstrate that vortex solitons in nonlinear media under competing self-focusing cubic and self-defocusing quintic nonlocal nonlinearities can be stabilized with a finite degree of nonlocality. Stable vortex solitons in the upper branch, bifurcated from the competing cubic-quintic nonlinearities, are found to be supported when the original d...

In this paper we show that the polynomial structure of the topological string partition function found by Yamaguchi and Yau for the quintic holds for an arbitrary Calabi-Yau manifold with any number of moduli. Furthermore, we generalize these results to the open topological string partition function as discussed recently by Walcher and reproduce his results for the real quintic.

We investigate properties of dark solitons under competing nonlocal cubic-local quintic nonlinearities. Analytical results, based on a variational approach and confirmed by direct numerical simulations, reveal the existence of a unique dark soliton solutions with their width being independent of the degree of nonlocality, due to the competing cubic-quintic nonlinearities.

I USE the term covariants to include invariants, and I write particularly concerning lists of covariants (groundforms) of the binary quintic and sextic, those of quantics of lower degree being few and well known. When the weight of a covariant is spoken of in this article, it must be understood to mean the weight of its first term or "source." The symbol 5ft will denote that covariant of the qu...

We show that a parametrically driven cubic-quintic complex Ginzburg-Landau equation exhibits a hysteretic nonequilibrium Ising-Bloch transition for large enough quintic nonlinearity. These results help to understand the recent experimental observation of this phenomenon [A. Esteban-Martín, Phys. Rev. Lett. 94, 223903 (2005)].

Using the Fermi Golden Rule analysis developed in [CM], we prove asymptotic stability of asymmetric nonlinear bound states bifurcating from linear bound states for a quintic nonlinear Schrödinger operator with symmetric potential. This goes in the direction of proving that the approximate periodic solutions for the cubic Nonlinear Schrödinger Equation (NLSE) with symmetric potential in [MW] do ...

We study, analytically, the discrete complex cubic–quintic Ginzburg–Landau (dCCQGL) equation with a non-local quintic term. We find a set of exact solutions which includes, as particular cases, bright and dark soliton solutions, constant magnitude solutions with phase shifts, periodic solutions in terms of elliptic Jacobi functions in general forms, and various particular periodic solutions.  ...

The modulation instability of the one-dimensional cubic-quintic complex Ginzburg-Landau equation with fouth-order dispersion and gain terms, a. k. a., the quintic complex Swift-Hohenberg equation, is investgated. The effects of the fourth-order terms to the modulational instability is studied. We numerically investigate the dynamics of the modulational instability in the presence of the fourtho...

We have numerically calculated the resonance curve and the region of existence of high-energy dissipative solitons in systems governed by the complex cubic-quintic Ginzburg-Landau equation. The calculations are carried out for negative reactive quintic nonlinearity. This choice allows the resonance curve to be continued into the region of positive net dispersion, thus showing that high-energy p...