Volume 3, Issue 4
Computation of Stationary Pulse Solutions of the Cubic-Quintic Complex Ginzburg-Landau Equation by a

Y.Y. CAO AND K.W. CHUNG

Int. J. Numer. Anal. Mod. B, 3 (2012), pp. 429-441

Published online: 2012-03

Export citation
  • Abstract
Stationary pulse solutions of the cubic-quintic complex Ginzburg-Landau equation are related to heteroclinic orbits in a three-dimensional dynamical systems and they are usually obtained using numerical simulation. The harmonic balance method has severe limitation in computing homoclinic/heteroclinic orbits since the period of such orbits is infinite. In this paper, we present a perturbation-incremental method to find such stationary pulse solutions. With the introduction of a nonlinear transformation, perturbed analytical pulse solutions are obtained in terms of trigonometric functions. Such formulation makes it possible to apply the harmonic balance method to find accurate approximate solutions of the corresponding heteroclinic orbits with arbitrary parametric values. Zero-order analytical solutions from the perturbation step and approximate solutions from the incremental step are compared with that from the bifurcation package AUTO, and they are in good agreement.
  • AMS Subject Headings

35A20 35Q56 37C29

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{IJNAMB-3-429, author = {Y.Y. CAO AND K.W. CHUNG}, title = {Computation of Stationary Pulse Solutions of the Cubic-Quintic Complex Ginzburg-Landau Equation by a}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2012}, volume = {3}, number = {4}, pages = {429--441}, abstract = {Stationary pulse solutions of the cubic-quintic complex Ginzburg-Landau equation are related to heteroclinic orbits in a three-dimensional dynamical systems and they are usually obtained using numerical simulation. The harmonic balance method has severe limitation in computing homoclinic/heteroclinic orbits since the period of such orbits is infinite. In this paper, we present a perturbation-incremental method to find such stationary pulse solutions. With the introduction of a nonlinear transformation, perturbed analytical pulse solutions are obtained in terms of trigonometric functions. Such formulation makes it possible to apply the harmonic balance method to find accurate approximate solutions of the corresponding heteroclinic orbits with arbitrary parametric values. Zero-order analytical solutions from the perturbation step and approximate solutions from the incremental step are compared with that from the bifurcation package AUTO, and they are in good agreement.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/293.html} }
TY - JOUR T1 - Computation of Stationary Pulse Solutions of the Cubic-Quintic Complex Ginzburg-Landau Equation by a AU - Y.Y. CAO AND K.W. CHUNG JO - International Journal of Numerical Analysis Modeling Series B VL - 4 SP - 429 EP - 441 PY - 2012 DA - 2012/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/293.html KW - Cubic-quintic complex Ginzburg-Landau equation KW - homoclinic ⁄ heteroclinic orbit KW - perturbation-incremental method KW - pulse AB - Stationary pulse solutions of the cubic-quintic complex Ginzburg-Landau equation are related to heteroclinic orbits in a three-dimensional dynamical systems and they are usually obtained using numerical simulation. The harmonic balance method has severe limitation in computing homoclinic/heteroclinic orbits since the period of such orbits is infinite. In this paper, we present a perturbation-incremental method to find such stationary pulse solutions. With the introduction of a nonlinear transformation, perturbed analytical pulse solutions are obtained in terms of trigonometric functions. Such formulation makes it possible to apply the harmonic balance method to find accurate approximate solutions of the corresponding heteroclinic orbits with arbitrary parametric values. Zero-order analytical solutions from the perturbation step and approximate solutions from the incremental step are compared with that from the bifurcation package AUTO, and they are in good agreement.
Y.Y. CAO AND K.W. CHUNG. (2012). Computation of Stationary Pulse Solutions of the Cubic-Quintic Complex Ginzburg-Landau Equation by a. International Journal of Numerical Analysis Modeling Series B. 3 (4). 429-441. doi:
Copy to clipboard
The citation has been copied to your clipboard