Wave-packet Dynamics in One-dimensional Nonlinear Schr¨odinger Lattices: Local vs. Nonlocal Nonlinear Effects

다국어 초록 (Multilingual Abstract)

We study numerically the dynamics of an initially localized wave packet in one-dimensional nonlinearSchr¨odinger lattices with both local and nonlocal nonlinearities. Using the discrete nonlinearSchr¨odinger equation generalized by including a nonlocal nonlinear term, we calculate four differentphysical quantities as a function of time, which are the return probability to the initial excitationsite, the participation number, the root-mean-square displacement from the excitation site and thespatial probability distribution. We investigate the influence of the nonlocal nonlinearity on thedelocalization to self-trapping transition induced by the local nonlinearity. In the non-self-trappingregion, we find that the nonlocal nonlinearity compresses the soliton width and slows down thespreading of the wave packet. In the vicinity of the delocalization to self-trapping transition pointand inside the self-trapping region, we find that a new kind of self-trapping phenomenon, which wecall partial self-trapping, takes place when the nonlocal nonlinearity is sufficiently strong.

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