Document Type

Journal article

Source Publication

Physics Letters A

Publication Date

12-28-2009

Volume

374

Issue

2

First Page

258

Last Page

263

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

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

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