Nonlinear optical waves with the second Painleve transcendent shape, associated with the complex cubic Ginzburg-Landau system

This study presents nonlinear optical waves with the second Painleve transcendent shape, described by the reduced complex cubic Ginzburg-Landau equation, whose reduction lies in neglecting both the spectral filtering and the nonlinear absorption. In this work, the authors impose a special requirement, including unknown coordinate functions S(z) and T(z), on the phase φ(z,τ) of a wave packet in the complex cubic Ginzburg-Landau system.