TY - JOUR
T1 - Stabilizing effects of dispersion management
AU - Zharnitsky, Vadim
AU - Grenier, Emmanuel
AU - Jones, Christopher K.R.T.
AU - Turitsyn, Sergei K.
N1 - Funding Information:
We would like to thank Yan Guo, Alejandro Aceves, and Taras Lacoba for many helpful discussions on this subject. We are also grateful to Markus Kunze for reading the manuscript and pointing out an error. V. Zharnitsky’s research was supported by NSF under Grant No. DMS-9627721 and No. DMS-9704906. C. Jones was supported by NSF under Grant No. DMS-9704906.
PY - 2001/5/15
Y1 - 2001/5/15
N2 - A cubic nonlinear Schrödinger equation (NLS) with periodically varying dispersion coefficient, as it arises in the context of fiber-optics communication, is considered. For sufficiently strong variation, corresponding to the so-called strong dispersion management regime, the equation possesses pulse-like solutions which evolve nearly periodically. This phenomenon is explained by constructing ground states for the averaged variational principle and justifying the averaging procedure. Furthermore, it is shown that in certain critical cases (e.g. quintic nonlinearity in one dimension and cubic nonlinearity in two dimensions) the dispersion management technique stabilizes the pulses which otherwise would be unstable. This observation seems to be new and is reminiscent of the well-known Kapitza's effect of stabilizing the inverted pendulum by rapidly moving its pivot.
AB - A cubic nonlinear Schrödinger equation (NLS) with periodically varying dispersion coefficient, as it arises in the context of fiber-optics communication, is considered. For sufficiently strong variation, corresponding to the so-called strong dispersion management regime, the equation possesses pulse-like solutions which evolve nearly periodically. This phenomenon is explained by constructing ground states for the averaged variational principle and justifying the averaging procedure. Furthermore, it is shown that in certain critical cases (e.g. quintic nonlinearity in one dimension and cubic nonlinearity in two dimensions) the dispersion management technique stabilizes the pulses which otherwise would be unstable. This observation seems to be new and is reminiscent of the well-known Kapitza's effect of stabilizing the inverted pendulum by rapidly moving its pivot.
KW - Dispersion management
KW - Ground states
KW - Nonlinear
KW - Schrödinger equation
KW - Stabilizing effect
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U2 - 10.1016/S0167-2789(01)00213-5
DO - 10.1016/S0167-2789(01)00213-5
M3 - Article
AN - SCOPUS:0035873348
SN - 0167-2789
VL - 152-153
SP - 794
EP - 817
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
ER -