Abstract We show that the solution (in sense of distribution) to Cauchy problem with periodic boundary condition associated modified Benjamin–Ono equation is unique in $L^\infty _t(H^s(\mathbb{T} ))$ for $s>1/2$. The proof based on analysis a normal form obtained by infinitely many reduction steps using integration parts time after suitable gauge transform.

In this paper, we study the Cauchy problem for Benjamin-Ono-Burgers equation $${\partial _t}u - \epsilon \partial _x^2u + {\cal H}\partial u{u_x} = 0$$ , where $${\cal H}$$ denotes Hilbert transform operator. We obtain that it is uniformly locally well-posed small data in refined Sobolev space $${\tilde H^\sigma }(\mathbb{R})\,\,(\sigma \geqslant 0)$$ which a subspace of L2(ℝ). It worth noting ...

We propose a novel class of arbitrarily high-order mass or energy conservative numerical schemes for the generalized Benjamin–Ono equation on whole real line. The spatial discretization is achieved by pseudo-spectral method with rational basis functions. By reformulating discretized system into different equivalent forms, either semi-discretized can be preserved exactly under continuous time fl...

Abstract We consider the third order Benjamin-Ono equation on torus ? t u = x ( ? 3 2 H ) + . prove that for any ? R , flow map continuously extends to r 0 s T if ? but does not admit a continuous extension 1 Moreover, we show is weakly sequentially in > L then classify traveling wave solutions and study their orbital stability.