Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 258-263 |
| Number of pages | 6 |
| Journal | Physics Letters A |
| Volume | 374 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 28 Dec 2009 |
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Keywords
- 2D cubic Ginzburg–Landau equation; Homoclinic orbits; Heteroclinic orbits; Hyperbolic property; Linearized stability; Hirota's bilinear transformation
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Novel homoclinic and heteroclinic solutions for the 2D complex cubic Ginzburg–Landau equation. / HUANG, Jian; LENG, Mingming; DAI, Zhengde.
In: Physics Letters A, Vol. 374, No. 2, 28.12.2009, p. 258-263.Research output: Journal Publications › Journal Article (refereed)
TY - JOUR
T1 - Novel homoclinic and heteroclinic solutions for the 2D complex cubic Ginzburg–Landau equation
AU - HUANG, Jian
AU - LENG, Mingming
AU - DAI, Zhengde
PY - 2009/12/28
Y1 - 2009/12/28
N2 - 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.
AB - 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.
KW - 2D cubic Ginzburg–Landau equation; Homoclinic orbits; Heteroclinic orbits; Hyperbolic property; Linearized stability; Hirota's bilinear transformation
UR - http://commons.ln.edu.hk/sw_master/1615
U2 - 10.1016/j.physleta.2009.10.069
DO - 10.1016/j.physleta.2009.10.069
M3 - Journal Article (refereed)
VL - 374
SP - 258
EP - 263
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
SN - 0375-9601
IS - 2
ER -