Benjamin--Ono-related equations and their solutions

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

An Improved Bilinear Estimate for Benjamin-ono Type Equations

A bilinear estimate in Fourier restriction norm spaces with applications to the Cauchy problem ut − |D| αux + uux = 0 in (−T, T ) × R u(0) = u0 is proved, for 1 < α < 2. As a consequence, local well-posedness in H(R) ∩ Ḣ(R) follows for s > − 3 4 (α − 1) and ω = 1/α − 1/2 This extends to global well-posedness for all s ≥ 0.

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.

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.

Time-Periodic Solutions of the Benjamin-Ono Equation

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...