Browsing by Autor "Orazio Descalzi"

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    Dissipative solitons onset through modulational instability of the cubic complex Ginzburg–Landau equation with nonlinear gradients
    (American Institute of Physics, 2025) M. I. Carvalho; M. Facão; Orazio Descalzi
    Modulation instability (MI) of the continuous wave (cw) has been associated with the onset of stable solitons in conservative and dissipative systems. The cubic complex Ginzburg-Landau equation (CGLE) is a prototype of a damped, driven, nonlinear, and dispersive system. The inclusion of nonlinear gradients is essential to stabilize pulses whether stationary or oscillatory. The soliton solutions of this model have been reasonably studied; however, its cw solution characteristics and stability have not been reported yet. Here, we obtain the cw solutions of the cubic CGLE with nonlinear gradient terms and study its short- and long-term evolution under the effect of small perturbations. We have found that, for each admissible amplitude, there are two branches of cw solutions, and all of them are unstable. Then, through direct integration of the evolution equation, we study the evolution of those cw solutions, observing the emergence of plain and oscillatory solitons. Depending on whether the cw and/or its perturbation are sinusoidal, we can obtain a train of a finite number of pulses or bound states.
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    The transition to explosive solitons and the destruction of invariant tori
    (De Gruyter Open, 2012) Jaime Cisternas; Orazio Descalzi; Carlos Cartes
    Abstract We investigate the transition to explosive dissipative solitons and the destruction of invariant tori in the complex cubic-quintic Ginzburg-Landau equation in the regime of anomalous linear dispersion as a function of the distance from linear onset. Using Poncaré sections, we sequentially find fixed points, quasiperiodicity (two incommesurate frequencies), frequency locking, two torus-doubling bifurcations (from a torus to a 2-fold torus and from a 2-fold torus to a 4-fold torus), the destruction of a 4-fold torus leading to non-explosive chaos, and finally explosive solitons. A narrow window, in which a 3-fold torus appears, is also observed inside the chaotic region.