TY - JOUR
T1 - Stability and interactions of pulses in simplified Ginzburg-Landau equations
AU - Malomed, Boris A.
AU - Gölles, Michael
AU - Uzunov, Ivan M.
AU - Lederer, Falk
PY - 1997
Y1 - 1997
N2 - We consider in detail two special types of the parameter-free Ginzburg-Landau equation, viz., the ones that combine the bandwidth-limited linear gain and nonlinear dispersion, or the broadband gain, linear dispersion, and nonlinear losses. The models have applications in nonlinear fiber optics and traveling-wave convection. They have exact solitary-pulse solutions which are subject to a background instability. In the former model, we find that the solitary pulse is much more stable than a "densely packed" multi-pulse array. On the contrary to this, a multi-pulse array in the latter model is destroyed by the instability very slowly. Considering bound states of two pulses, we conclude that they may form a robust bound state in both models. Conditions which allow for formation of the bound states qualitatively differ in the two models.
AB - We consider in detail two special types of the parameter-free Ginzburg-Landau equation, viz., the ones that combine the bandwidth-limited linear gain and nonlinear dispersion, or the broadband gain, linear dispersion, and nonlinear losses. The models have applications in nonlinear fiber optics and traveling-wave convection. They have exact solitary-pulse solutions which are subject to a background instability. In the former model, we find that the solitary pulse is much more stable than a "densely packed" multi-pulse array. On the contrary to this, a multi-pulse array in the latter model is destroyed by the instability very slowly. Considering bound states of two pulses, we conclude that they may form a robust bound state in both models. Conditions which allow for formation of the bound states qualitatively differ in the two models.
UR - http://www.scopus.com/inward/record.url?scp=3343004204&partnerID=8YFLogxK
U2 - 10.1088/0031-8949/55/1/012
DO - 10.1088/0031-8949/55/1/012
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AN - SCOPUS:3343004204
VL - 55
SP - 73
EP - 79
JO - Physica Scripta
JF - Physica Scripta
SN - 0031-8949
IS - 1
ER -