Abstract
Sasa–Satsuma equation (SSE) is one of the nontrivial integrable extensions of nonlinear Schrödinger equation including third order dispersion, self-frequency shift and self-steepening. The hierarchy of Nth-order semi-rational solutions with 3N free parameters of SSE can be calculated theoretically through a modified dressing transformation associated with a novel expansion technique. The Bloch eigenfunction is introduced and Schur multinomial is invoked. When the free parameters satisfy some constraints, these solutions can be reduced to pure rational solutions so as to study the dynamics of rogue waves. In addition, triangular and elliptical multi-rogue wave patterns in either single-peak or double-peak case are examined smoothly. On the other hand, the semi-rational solutions allow us to investigate various interesting superimposed scenes between rogue waves and breathers. These results may contribute to demonstrating the rogue wave phenomenon emerging in water waves, optical fibers and generally in dispersive nonlinear media.
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