The Dynamics of Lump, Lumpoff and Rogue Wave Solutions of (2+1)-Dimensional Hirota-Satsuma-Ito Equations

Abstract

The Hirota-Satsuma-Ito equation in (2+1)-dimensions is studied and a new general representation of lump solutions is derived. If the lump soliton is generated by an exponentially localised line soliton, we obtain a lumpoff solution. On the other hand, if the lump soliton is generated by an exponentially localised twin plane soliton, we obtain a rogue solution. The appearance time and location of extreme rogue waves can be studied and predicted. Graphical examples demonstrate the dynamical behaviour of lumpoff and rogue waves.