Generalized Solutions of the Benjamin-Ono and Smith Equations

Generalized solutions to the Benjamin-Ono equations in sense of Colombeau.

This paper discusses the existence and uniqueness of the generalized solution in the sense of Colombeau to the Benjamin-Ono (B-O) equation and the relationship between the new generalized solution and the classical solution.

Low regularity solutions of the Benjamin-Ono and the KP-I equations

Blow up and instability of solitary wave solutions to a generalized Kadomtsev– Petviashvili equation and two-dimensional Benjamin–Ono equations

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...

Solitary waves of the rotation-generalized Benjamin-Ono equation

This work studies the rotation-generalized Benjamin-Ono equation which is derived from the theory of weakly nonlinear long surface and internal waves in deep water under the presence of rotation. It is shown that the solitary-wave solutions are orbitally stable for certain wave speeds.

Complex-valued Solutions of the Benjamin–ono Equation

We prove that the Benjamin–Ono initial-value problem is locally well-posed for small data in the Banach spaces H̃σ(R), σ ≥ 0, of complex-valued Sobolev functions with special low-frequency structure.