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- W2079971818 abstract "The nonlinear Schrodinger equation $i{ensuremath{partial}}_{z}A(z,x,t)+{ensuremath{nabla}}_{x,t}^{2}A+[1+m(ensuremath{kappa}x)]|A{|}^{2}A=0$ 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 $ensuremath{kappa}=mathrm{text{beamwidth}}/mathrm{text{lattice period}}$. Wide ($ensuremath{kappa}ensuremath{gg}1$) and $ensuremath{kappa}=O(1)$ 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.''" @default.
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- W2079971818 date "2006-11-08" @default.
- W2079971818 modified "2023-09-25" @default.
- W2079971818 title "Waves in Nonlinear Lattices: Ultrashort Optical Pulses and Bose-Einstein Condensates" @default.
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- W2079971818 doi "https://doi.org/10.1103/physrevlett.97.193902" @default.
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