Document Type
Journal article
Source Publication
Physics Letters A
Publication Date
12-28-2009
Volume
374
Issue
2
First Page
258
Last Page
263
Publisher
Elsevier BV
Keywords
2D cubic Ginzburg–Landau equation; Homoclinic orbits; Heteroclinic orbits; Hyperbolic property; Linearized stability; Hirota's bilinear transformation
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.
DOI
10.1016/j.physleta.2009.10.069
Print ISSN
03759601
E-ISSN
18732429
Funding Information
This work is supported by NSFC (70901036) and the Croucher Foundation (RSD163/0809/S).
Publisher Statement
Copyright © 2009 Elsevier B.V. All rights reserved. Access to external full text or publisher's version may require subscription.
Full-text Version
Accepted Author Manuscript
Language
English
Recommended Citation
Huang, J., Leng, M., & Dai, Z. (2009). Novel homoclinic and heteroclinic solutions for the 2D complex cubic Ginzburg–Landau equation. Physics Letters A, 374(2), 258-263. doi: 10.1016/j.physleta.2009.10.069