Nonlinear Krönig-Penney model.
We study the nonlinear Schrödinger equation with a periodic delta-function potential. This realizes a nonlinear Krönig-Penney model, with physical applications in the context of trapped Bose-Einstein condensate alkaly gases and in the transmission of signals in optical fibers. We find analytical solutions of zero-current Bloch states. Such wave functions have the same periodicity of the potential, and, in the linear limit, reduce to the Bloch functions of the Krönig-Penney model. We also find classes of solutions having a periodicity different from that of the external potential. We calculate the chemical potential of such states and compare it with the linear excitation spectrum.
Istituto Nazionale per la Fisica della Materia BEC-CRS and Dipartimento di Fisica, Università di Trento, I-38050 Povo, Italy.
WeiDong
W
Li
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A
Smerzi