Abstract:In this paper, the bifurcation theory of dynamical system is applied to investigate the time-space fractional complex Ginzburg-Landau equation with Kerr law nonlinearity. We mainly consider the case of α ≠ 2β which is not discussed in previous work. By overcoming some difficulties aroused by the singular traveling wave system, such as bifurcation analysis of nonanalytic vector field, tracking orbits near the full degenerate equilibrium and calculation of complicated elliptic integrals, we give a total of 20 ex… Show more
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