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.

We study the Cauchy initial-value problem for the Benjamin-Ono equation in the zero-dispersion limit, and we establish the existence of this limit in a certain weak sense by developing an appropriate analogue of the method invented by Lax and Levermore to analyze the corresponding limit for the Korteweg–de Vries equation. © 2010 Wiley Periodicals, Inc.

We present a spectrally accurate numerical method for finding non-trivial timeperiodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the in...

A hierarchy of pairwise commuting Hamiltonians for the quantum periodic Benjamin–Ono equation is constructed by using the Lax matrix. The eigenvectors of these Hamiltonians are Jack symmetric functions of infinitely many variables x1, x2, . . .. This construction provides explicit expressions for the Hamiltonians in terms of the power sum symmetric functions pn = x n 1 + x n 2 + · · · and is ba...

An alternative type of nonlinear evolution equation is derived that describes interfacial waves in a two-layer fiuid system. The equation presented here is a higher-order version of the Benjamin-Ono (BO) equation. A solitary-wave solution of the equation is obtained by means of a singular perturbation method. The characteristics of the solution are discussed in comparison with those for a highe...

We present a spectrally accurate numerical method for finding non-trivial timeperiodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the in...