Novel homoclinic and heteroclinic solutions for the 2D complex cubic Ginzburgâ•fiLandau equation
نویسندگان
چکیده
Homoclinic and heteroclinic solutions are two important concepts that are used to investigate the complex properties of nonlinear evolutionary equations. In this paper, we perform hyperbolic and linear stability analysis, and prove the existence of homoclinic and heteroclinic solutions for two-dimensional cubic Ginzburg-Landau equation with periodic boundary condition and even constraint. Then, using the Hirota’s bilinear transformation, we find the closed-form homoclinic and heteroclinic solutions. Moreover, we find that the homoclinic tubes (which are formed by a pair of symmetric homoclinic solutions) and two families of heteroclinic solutions are asymptotic to a periodic cycle in one dimension.
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