Analytic Solutions of 2D Cubic Quintic Complex Ginzburg-Landau Equation

Figure 1

Phase portrait for different values of in (a) and (b) for five equilibrium points, and corresponding potentials in (c) and (d). In (a), one has the heteroclinic orbit, which is the curve starting at one fixed point and ending at another fixed point predicting the existence of kink or dark soliton as solution. In (b), one has the separatrix which appears as the combination of homoclinic and heteroclinic orbits, predicting then the existence of a bright-dark soliton pair as solution. This last case, due to the presence of the quintic term, cannot be obtained in the cubic case as in [28].

(a)

(b)

(c)

(d)