Rogue waves and hybrid solutions of the Davey–Stewartson I equation

Abstract

Explicit forms of rogue waves and hybrid solutions of the Davey–Stewartson I (DS I) equation are derived by performing an appropriate limiting procedure on soliton solutions that are generated by the Hirota bilinear method. Using this method, many interesting, from the physical point of view, hybrid solutions are constructed. The hybrid solutions illustrate various superimposed wave structures involving rogue waves, lumps, solitons, and periodic line waves. The unique ( $$2+1$$ )-dimensional dynamics of the obtained exact solutions of the DS I equation may help to understand the formation and key properties of rogue waves in many other physical settings.