Analysis shows distinct rogue wave patterns in the Boussinesq equation, suggesting new insights into nonlinear equations.
We study higher-order rogue wave patterns for the well-known Boussinesq equation for the cases where the solution parameters are large. We show that these consist of a collection of individual fundamental rogue waves arranged in circles. The radii of these circles are found from the zeroes of certain polynomials. Finally, we briefly compare the patterns found with those of higher-order rogue wave patterns of the nonlinear-Schrödinger (NLS) and other equations. Abstract Published by the Jagiellonian University 2025 authors
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Adrian Ankiewicz (2025) studied this question.
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