TY - JOUR
T1 - Regularization and control of self-focusing in the 2D cubic Schrodinger equation by attractive linear potentials
AU - LeMesurier, B.
AU - Christiansen, Peter Leth
PY - 2003
Y1 - 2003
N2 - The self-focusing singularity of the attractive 2D cubic Schrödinger equation arises in nonlinear optics and many other situations, including certain models of Bose-Einstein condensates. This 2D case is very sensitive to perturbations of the equation and so solutions can be regularized in a number of ways. Here the effect of linear potentials is considered, such as could arise in models of optical fibres with narrow cores of different refractive index, wave-guides induced in a nonlinear medium by another beam, and as part of the Gross-Pitaevskii model of Bose-Einstein condensates. It is observed that in critical dimension only, one can have inhibition of collapse by attractive linear potentials, without dissipation, and that this can lead to a stable oscillating beam, as opposed to the dispersion or dissipation seen with previously studied regularizing mechanisms.
AB - The self-focusing singularity of the attractive 2D cubic Schrödinger equation arises in nonlinear optics and many other situations, including certain models of Bose-Einstein condensates. This 2D case is very sensitive to perturbations of the equation and so solutions can be regularized in a number of ways. Here the effect of linear potentials is considered, such as could arise in models of optical fibres with narrow cores of different refractive index, wave-guides induced in a nonlinear medium by another beam, and as part of the Gross-Pitaevskii model of Bose-Einstein condensates. It is observed that in critical dimension only, one can have inhibition of collapse by attractive linear potentials, without dissipation, and that this can lead to a stable oscillating beam, as opposed to the dispersion or dissipation seen with previously studied regularizing mechanisms.
U2 - 10.1016/S0167-2789(03)00222-7
DO - 10.1016/S0167-2789(03)00222-7
M3 - Journal article
SN - 0167-2789
VL - 184
SP - 226
EP - 236
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 1-4
ER -