Rogue Wave Patterns for Boussinesq and Other Physical 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