We present three novel pulsating solutions of the cubic-quintic complex Ginzburg-Landau equation. They describe some complicated pulsating behavior of solitons in dissipative systems. We study their main features and the regions of parameter space where they exist.

We consider the Taubes correspondencebetween solutions of the Seiberg– Witten equations on a compact 4-dimensional symplectic manifold and pseudoholomorphic curves on this manifold. We compare it with its 3-dimensional analogue in which the roles of Seiberg–Witten equations and pseudoholomorphic curves are played respectively by the Ginzburg–Landau equations and adiabatic paths in the moduli sp...

The discrete complex Ginzburg-Landau equation is a fundamental model for the dynamics of nonlinear lattices incorporating competitive dissipation and energy gain effects. Such mechanisms are particular importance study survival/destruction localised structures in many physical situations. In this work, we prove that dissipative solitonic waveforms persist significant times by introducing dynami...

A new description is proposed for the low-field critical behavior of type-II superconductors. The starting point is the Ginzburg-Landau theory in presence of an external magnetic field H. A set of fictitious vortex variables and a singular gauge transformation are used to rewrite a finite H Ginzburg-Landau functional in terms of a complex scalar field of zero average vorticity. The continuum li...

Spatially localized, time-periodic structures are common in pattern-forming systems, appearing in fluid mechanics, chemical reactions, and granular media. We examine the existence of oscillatory localized states in a PDE model with single frequency time dependent forcing, introduced in [22] as phenomenological model of the Faraday wave experiment. In this study, we reduce the PDE model to the f...