TY - JOUR

T1 - Waves in nonlinear lattices

T2 - Ultrashort optical pulses and Bose-Einstein condensates

AU - Sivan, Y.

AU - Fibich, G.

AU - Weinstein, M. I.

PY - 2006/11/16

Y1 - 2006/11/16

N2 - The nonlinear Schrödinger equation i ∂ zA(z,x,t)+ x,t2A+[1+m(κx)]|A|2A=0 models the propagation of ultrashort laser pulses in a planar waveguide for which the Kerr nonlinearity varies along the transverse coordinate x, 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 κ=beamwidth/lattice period. Wide (κ+/1) and κ=O(1) bound states centered at a maximum of m(x) are unstable, as they violate the slope condition. Bound states centered at a minimum of m(x) violate the spectral condition, resulting in a drift instability. Thus, a nonlinear lattice can only stabilize narrow bound states centered at a maximum of m(x). Even in that case, the stability region is so small that these bound states are "mathematically stable" but "physically unstable."

AB - The nonlinear Schrödinger equation i ∂ zA(z,x,t)+ x,t2A+[1+m(κx)]|A|2A=0 models the propagation of ultrashort laser pulses in a planar waveguide for which the Kerr nonlinearity varies along the transverse coordinate x, 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 κ=beamwidth/lattice period. Wide (κ+/1) and κ=O(1) bound states centered at a maximum of m(x) are unstable, as they violate the slope condition. Bound states centered at a minimum of m(x) violate the spectral condition, resulting in a drift instability. Thus, a nonlinear lattice can only stabilize narrow bound states centered at a maximum of m(x). Even in that case, the stability region is so small that these bound states are "mathematically stable" but "physically unstable."

UR - http://www.scopus.com/inward/record.url?scp=33750901302&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.97.193902

DO - 10.1103/PhysRevLett.97.193902

M3 - Article

C2 - 17155630

AN - SCOPUS:33750901302

SN - 0031-9007

VL - 97

JO - Physical Review Letters

JF - Physical Review Letters

IS - 19

M1 - 193902

ER -