Exact solutions of the one-dimensional quintic complex Ginzburg-Landau equation

Abstract

Exact solitary wave solutions of the one-dimensional quintic complex Ginzburg-Landau equation are obtained using a method derived from the Painlevé test for integrability. These solutions are expressed in terms of hyperbolic functions, and include the pulses and fronts found by van Saarloos and Hohenberg. We also find previously unknown sources and sinks. The emphasis is put on the systematic character of the method which breaks away from approaches involving somewhat ad hoc Ansätze.

Ginzburg-Landau system of complex modulation equations for distributed nonlinear dissipative transmission lines

“…Sources and sinks connect, asymptotically, plane waves, and so the corresponding orbits in the ordinary differential equations connect fixed points. Many different coherent structures have been identified within this framework [21][22][23][24][25][26].…”

Explicit and implicit solutions for the one-dimensional cubic and quintic complex Ginzburg–Landau equations

“…The CGL can be thought of as a normal form for a Hopf bifurcation in a variety of spatially extended systems [2]. In fact, the amplitude w describes slow modulations in space and time of the underlying bifurcating spatially periodic pattern [4].…”

Modeling Frequency Comb Sources

“…An extra benefit of introducing high-order effects is that stable soliton solutions can be found even if the gain is constant [50,51]. The QCGLE has been discussed thoroughly and extensively not only in optical systems but also many nonequilibrium physical systems to investigate the instabilities [43,52,53]. The pulses described by (4) are no longer the analytical solutions of QCGLE.…”