Soliton and breather solutions of the Sasa–Satsuma equation via the Darboux transformation

Abstract

In this paper, we construct the general Darboux transformation on the Sasa–Satsuma equation and represent the iterated solutions in terms of the three-component Wronskian. From the once-iterated solution, we derive the breather as well as the single- and double-hump solitons. We also analyze three types of collisions: soliton–soliton, breather–breather and soliton–breather collisions. The surprising result is that the soliton–breather collision may exhibit the shape-changing phenomena, that is, one breather (or soliton) may change into a soliton (or breather) when interacting with another breather. Such novel collision phenomena may be applied in all-optical information processing, optical switching and routing of optical signals.