Lump, lumpoff and predictable rogue wave solutions to a dimensionally reduced Hirota bilinear equation*

Abstract

We study a simplified (3+1)-dimensional model equation and construct a lump solution for the special case of z = y using the Hirota bilinear method. Then, a more general form of lump solution is constructed, which contains more arbitrary autocephalous parameters. In addition, a lumpoff solution is also derived based on the general lump solutions and a stripe soliton. Furthermore, we figure out instanton/rogue wave solutions via introducing two stripe solitons. Finally, one can better illustrate these propagation phenomena of these solutions by analyzing images.