Remarks on the two-dimensional Benjamin equation

Two Remarks on the Generalised Korteweg De-vries Equation

We make two observations concerning the generalised Korteweg de Vries equation ut + uxxx = μ(|u|u)x. Firstly we give a scaling argument that shows, roughly speaking, that any quantitative scattering result for L-critical equation (p = 5) automatically implies an analogous scattering result for the L-critical nonlinear Schrödinger equation iut+uxx = μ|u|4u. Secondly, in the defocusing case μ > 0...

Remarks on the Schrödinger Equation

Various origins of linear and nonlinear Schrödinger equations are discussed in connection with diffusion, hydrodynamics, and fractal structure. The treatment is mainly expository, emphasizing the quantum potential, with a few new observations.

Remarks on the Wdw Equation

We show a kind of converse to some results of Hall and Reginatto on exact uncertainty related to the Schrödinger and Wheeler-deWitt equations. Some survey material on statistical geometrodynam-ics is also sketched.

Benjamin-Ono Equation on a Half-Line

Remarks on the KLB theory of two-dimensional turbulence

We study the inverse energy transfer in forced two-dimensional (2D) Navier–Stokes turbulence in a doubly periodic domain. It is shown that an inverse energy cascade that carries a nonzero fraction of the injected energy to the large scales via a power-law energy spectrum ∝ k−α requires that α ≥ 5/3. This result is consistent with the classical theory of 2D turbulence that predicts a k−5/3 inver...