Rogue waves excitation on zero-background in the (2+1)-dimensional KdV equation

Abstract

In this letters, we propose a novel self-mapping transformation of the (2+1) dimensional KdV equation, and construct rather general classes of solutions with decaying property with three arbitrary functions of time. The highlight of this method is that it allows us to generate various of basic rogue waves excited on zero-background, including the exponentially decaying line-soliton and dromion as well as the algebraically decaying lump in the -plane turn out to be special cases of these solutions. Our findings unravels new interesting relations between rogue wave and line-soliton, dromion and lump.