Proposed model describes localized ocean wave solutions with an exponential term, indicating dynamic behavior.
We propose a one-dimensional nonlinear Schr¨odinger equation containing an exponential imaginary term associated with ocean wave intensity. The model admits localized solutions with exponential growth, analogous to waterspouts. The width dynamics leads to an Ermakov-type equation and a generalized Ermakov–Lewis invariant.
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Daniel Gemaque da Silva (2026) studied this question.