A special set of N -coupled nonlinear Schrödinger equations which consists of 2 N interaction types each of which is characterized by a specific array of interaction parameters is presented. It is shown that every Lamé function of order n ≤ N is a solution for one or more components for one or more interaction types of this special set. Simple rules that relate interaction and solution types and interesting features of these relationships are presented.
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Hioe et al. (2002) studied this question.
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