Ascertain wave patterns for determinant rogue waves with Schur index jumps of three under multiple large parameters

Ascertain the spatial–temporal wave patterns of rogue waves in integrable systems whose solutions are expressible as determinants featuring Schur polynomials with index jumps of three (for example, the Manakov equations and the three-wave resonant interaction system) when multiple internal parameters are large, extending beyond the single-parameter case described by Okamoto polynomial hierarchies.

Background

For integrable systems with rogue-wave solutions given by determinants involving Schur polynomials with index jumps of three, prior work has shown that when a single internal parameter is large, the pattern is governed by the root structures of Okamoto polynomial hierarchies.

The authors emphasize that, unlike the single-parameter setting, the case of multiple large internal parameters in these systems has not been characterized, and they point to this as an open direction that may be approachable by extending the methods developed in this paper.