Dispersive shock waves for the Boussinesq Benjamin–Ono equation

In this work, the dispersive shock wave (DSW) solution of a Boussinesq Benjamin–Ono (BBO) equation, standard equation with dispersion replaced by nonlocal dispersion, is derived. This DSW derived using two methods, fitting and from simple Whitham modulation equations for BBO equation. The first these yields edges DSW, while second complete solution. As could not be set in Riemann invariant form, ordinary differential governing are solved hybrid numerical method coupled to which provides suitable boundary condition. full then determined, found excellent agreement solutions relatively fully determine nonlinear (hyperbolic) known, but their form not.