Semi-rational solutions of the third-type Davey-Stewartson equation

摘要

General dark solitons and mixed solutions consisting of dark solitons andbreathers for the third-type Davey-Stewartson (DS-III) equation are derived byemploying the bilinear method. By introducing the two differential operators,semi-rational solutions consisting of rogue waves, breathers and solitons aregenerated. These semi-rational solutions are given in terms of determinantswhose matrix elements have simple algebraic expressions. Under suitableparametric conditions, we derive general rogue wave solutions expressed interms of rational functions. It is shown that the fundamental (simplest) roguewaves are line rogue waves. It is also shown that the multi-rogue wavesdescribe interactions of several fundamental rogue waves, which would generateinteresting curvy wave patterns. The higher order rogue waves originate from alocalized lump and retreat back to it. Several types of hybrid solutionscomposed of rogue waves, breathers and solitons have also been illustrated.Specifically, these semi-rational solutions have a new phenomenon: lumps formon dark solitons and gradual separation from the dark solitons is observed.