States without a linear counterpart in Bose-Einstein condensates

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Abstract
We show the existence of stationary solutions of a one-dimensional Gross-Pitaevskii equation in the presence of a multiwell external potential that do not reduce to any of the eigenfunctions of the associated Schrödinger problem. These solutions, which in the limit of strong nonlinearity have the form of chains of dark or bright solitons located near the extrema of the potential, represent macroscopically excited states of a Bose-Einstein condensate and are in principle experimentally observable.