Abstract
The nonlinear Schrödinger equation models the propagation of ultrashort laser pulses in a planar waveguide for which the Kerr nonlinearity varies along the transverse coordinate , and also the evolution of 2D Bose-Einstein condensates in which the scattering length varies in one dimension. Stability of bound states depends on the value of . Wide () and bound states centered at a maximum of are unstable, as they violate the slope condition. Bound states centered at a minimum of violate the spectral condition, resulting in a drift instability. Thus, a nonlinear lattice can only stabilize narrow bound states centered at a maximum of . Even in that case, the stability region is so small that these bound states are “mathematically stable” but “physically unstable.”
- Received 24 April 2006
DOI:https://doi.org/10.1103/PhysRevLett.97.193902
©2006 American Physical Society