We consider the generalized Benjamin-Ono (gBO) equation on real line, $ u_t + \partial_x (-\mathcal H u_{x} \tfrac1{m} u^m) = 0, x \in \mathbb R, m 2,3,4,5$, and perform numerical study of its solutions. first compute ground state solution to $-Q -\mathcal Q^\prime +\frac1{m} Q^m 0$ via Petviashvili's iteration method. then investigate behavior solutions in ($m=2$) for initial data with differe...

The interaction of interfacial solitary waves of algebraic type is investigated on the basis of a higherorder Benjamin-Ono equation. By developing a multisoliton perturbation theory, we show analytically that the overtaking collision between two solitary waves exhibits the phase shift but the amplitudes are not altered after interaction. The predication of the phase shift that takes place betwe...

Abstract The BBM equation is a Hamiltonian PDE which revealed to be very interesting test-model study the transformation property of Gaussian measures along flow, after Tzvetkov (Sigma 3:e28-35). In this paper we with critical dispersion (which Benjamin-Ono type model). We prove that image supported on fractional Sobolev spaces increasing regularity are absolutely continuous, but cannot identif...

We shall deduce some special regularity properties of solutions to the IVP associated to the Benjamin-Ono equation. Mainly, for datum u0 ∈ H3/2(R) whose restriction belongs to Hm((b,∞)) for some m ∈ Z+, m≥ 2, and b ∈ R we shall prove that the restriction of the corresponding solution u(·, t) belongs to Hm((β ,∞)) for any β ∈R and any t > 0. Therefore, this type of regularity of the datum travel...