TY - JOUR
T1 - Stabilizing effects of dispersion management
AU - Zharnitsky, Vadim
AU - Grenier, Emmanuel
AU - Jones, Christopher K. R. T.
AU - Turitsyn, Sergei T.
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 - stabilizing effect
KW - disperion management
KW - nonlinear
KW - Schrödinger equation
KW - ground states
UR - http://www.scopus.com/inward/record.url?scp=0035873348&partnerID=8YFLogxK
UR - https://www.sciencedirect.com/science/article/pii/S0167278901002135?via%3Dihub
U2 - 10.1016/S0167-2789(01)00213-5
DO - 10.1016/S0167-2789(01)00213-5
M3 - Article
SN - 0167-2789
VL - 152-153
SP - 794
EP - 817
JO - Physica D
JF - Physica D
ER -