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Analysis reveals dynamics and polynomial relationships of rogue waves in the Davey–Stewartson I equation, suggesting new insights into wave behavior.
In this paper, we concentrate on the high‐order rogue waves of the Davey–Stewartson I equation and investigate their dynamics in great detail. The approximate trajectories of curvy rogue waves in the intermediate stage and certain lumps at large time are determined by a special polynomial which is expressed by some Schur polynomials and their derivatives. Besides, the number of lumps at large time is illustrated by using a positive integer partition and its corresponding Young diagram. The true and estimated results show excellent agreement.
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Wei et al. (2025) studied this question.
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