We consider a higher-dimensional version of the Benjamin-Ono (HBO) equation in 2D setting: , which is -critical, and investigate properties solutions both analytically numerically. For generalized (fractional gKdV) after deriving Pohozaev identities, we obtain nonexistence conditions for solitary wave solutions, then prove uniform bounds energy space or conditional global existence, radiation r...

Blow up and instability of solitary wave solutions to a generalized Kadomtsev– Petviashvili equation and two-dimensional Benjamin–Ono equations BY JIANQING CHEN*, BOLING GUO AND YONGQIAN HAN School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, People’s Republic of China Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, Peopl...

We show that the Benjamin-Ono equation is globally well-posed in H s (R) for s ≥ 1. This is despite the presence of the derivative in the non-linearity, which causes the solution map to not be uniformly continuous in H s for any s [15]. The main new ingredient is to perform a global gauge transformation which almost entirely eliminates this derivative.

We employ the idea of Hirota’s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of Multiple soliton solutions of secondorder Benjamin-Ono equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.