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Toda [1], Boyd [2], Zaitsev [3], Korpel & Banerjee [4], and Whitham [5] have proved that many species of solitons may be cloned and superposed with even spacing to generate exact nonlinear, spatially periodic solutions (“cnoidal waves”). The equations solved by such “imbricate” series of solitary waves include the Korteweg-deVries, Cubic Schroedinger, Benjamin-Ono, and resonant triad equations. However, all existing theorems apply only when the solitons are rational or meromorphic functions and the cnoidal waves are elliptic functions. In this note, we ask: does the exact soliton-superposition apply to non-elliptic solitons and cnoidal waves

Exact and approximate nonlinear waves generated by the periodic superposition of solitons