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Novel homoclinic and heteroclinic solutions for the 2D complex cubic Ginzburg-Landau equation |
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| Authors: | Jian Huang Mingming Leng |
| Affiliation: | a School of Information Technology, Jiangxi University of Finance and Economics, Nanchang, Jiangxi 330013, China b Department of Computing and Decision Sciences, Lingnan University, 8 Castle Peak Road, Tuen Mun, Hong Kong c School of Mathematics and Statistics, Yunnan University, Kunming, Yunnan 650091, China |
| Abstract: | Homoclinic and heteroclinic solutions are two important concepts that are used to investigate the complex properties of nonlinear evolutionary equations. In this Letter, 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 and two families of heteroclinic solutions are asymptotic to a periodic cycle in one dimension. |
| Keywords: | 05.45.Yv 02.30.Jr 02.30.Ik |
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