Multiple Lump and Rogue Wave Solutions of a Modified Benjamin-Ono Equation

In this chapter, a (2+1)-dimensional modified Benjamin-Ono (MBO) equation is introduced. Multiple lump (M-lump) and rogue wave solutions are obtained for the equation with the aid of the Hirota bilinear method. The equation is first studied in two parts: an integrable and a nonintegrable part. The nonintegrable part is found to possess 1-lump and line rogue wave solutions whereas the integrable part has only 1-lump solutions. Furthermore, the MBO equation is found to posses both multiple lump and rogue wave solutions. By fixing parameter values, the dynamics of the solutions are studied with 3D and density plots.