Temporal evolutions and stationary waves for dissipative Benjamin–Ono equation

Initial value problems as well as stationary solitary and periodic waves are investigated for dissipative Benjamin–Ono (DBO) equation. Multi-hump stationary waves and their structures are identified numerically and the stability regions of stationary periodic waves are also examined numerically. These results elucidate a close relation between irregular behaviours in the initial value problem and the multiplicity of stationary waves.