A (2 + 1)-dimensional extension of the Benjamin-Ono equation

Purpose The purpose of this paper is concerned with developing a (2 + 1)-dimensional Benjamin–Ono equation. The study shows that multiple soliton solutions exist and multiple complex soliton solutions exist for this equation. Design/methodology/approach The proposed model has been handled by using the Hirota’s method. Other techniques were used to obtain traveling wave solutions. Findings The examined extension of the Benjamin–Ono model features interesting results in propagation of waves and fluid flow. Research limitations/implications The paper presents a new efficient algorithm for constructing extended models which give a variety of multiple soliton solutions. Practical implications This work is entirely new and provides new findings, where although the new model gives multiple soliton solutions, it is nonintegrable. Originality/value The work develops two complete sets of multiple soliton solutions, the first set is real solitons, whereas the second set is complex solitons.