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 &#8260 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.