..., z, t}. The asymptotic analysis is presented to represent generally the evolutions of rogue waves. Findings Fixing several types of explicit expressions of the arbitrary function in the potential field U, various novel nonlinear wave excitations are fabricated, such as hybrid waves...

...Na Liu Purpose The purpose of this paper is to study the homoclinic breather waves, rogue waves and multi-soliton waves of the (2 + 1)-dimensional Mel’nikov equation, which describes an interaction of long waves with short wave packets. Design/methodology/approach The author applies...