A generalized form of (2+1)-dimensional Hirota bilinear (2D-HB) equation is considered herein in order to study nonlinear waves in fluids and oceans. The present goal is carried out through adopting the simplified Hirota’s method as well as ansatz approaches to retrieve a bunch of rational wave structures from multiple soliton solutions to breather, rogue, and complexiton solutions. Some figures corresponding to a series of rational wave structures are provided, illustrating attractive physical behaviors. Results of the current study reveal that the generalized 2D-HB equation is completely integrable and therefore guaranties the existence of multiple soliton solutions of any order.

No abstract