LAUSR

A periodically breather solitary wave and some lump solutions are obtained via using Hirota’s bilinear method, homoclinic test approach and parameter perturbation technique for the (1 + 1)-dimensional Benjamin–Ono equation. Spatiotemporal dynamics of lump solution is investigated and discussed by choice of some parameters $$u_{0}, \beta ,$$u0,β, and $$\gamma $$γ. Finally, spatiotemporal structure of lump solution is analyzed using the extreme value theory of multivariable function.