Properties of the Benjamin–Ono equation

Abstract

The question is raised as to whether the Benjamin–Ono equation, a nonlinear partial differential integral equation, is a completely integrable Hamiltonian system. The answer is almost certainly ’’yes.’’ Particular solutions suggest the form that general polynomial constants must have. The structure of these and an algorithm to compute them is given. Explicit formulas are given for the first six.

IST Versus PDE: A Comparative Study

“…As previously recalled, the BO equation has an infinite number of conserved quantities ( [44], the first ones are displayed in [1]). The Hamiltonian flow of those invariants define the aforementioned Benjamin-Ono hierarchy.…”

Statistical mechanics of the periodic Benjamin–Ono equation

“…Proposition 5.6 (Case [10]). Let (e iq j (t) ) n j=1 ∈ D n evolve according to the canonical equations (2.7), and suppose that η j (0) > 0.…”

Long time behavior for the equation of finite-depth fluids

“…In order to bound S τ (y) for all y e i?, we need the following classical Van der Corput lemma [14] Lemma 8. Suppose that φ £ Cl(R) and φ £ C 2 (R) such that \φ"(ξ)\^l on the support of φ. Then where the constant C is independent of λ, φ and φ.…”