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We present a first-principles derivation of the coupled nonlinear Schr\"odinger equations that govern the interaction between two families of modes with different transverse profiles in a generic whispering-gallery-mode resonator. We find regions of modulational instability and the existence of trains of bright solitons in both the normal and the anomalous dispersion regime.
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D’Aguanno et al. (2016) studied this question.
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