We study the Whitham equations for the defocusing complex modified KdV (mKdV) equation. These Whitham equations are quasilinear hyperbolic equations and they describe the averaged dynamics of the rapid oscillations which appear in the solution of the mKdV equation when the dispersive parameter is small. The oscillations are referred to as dispersive shocks. The Whitham equations for the mKdV eq...

The Whitham equation was proposed as a model for surface water waves that combines the quadratic flux nonlinearity $f(u) = \tfrac{1}{2}u^2$ of Korteweg-de Vries and full linear dispersion relation $\Omega(k) \sqrt{k\tanh k}$ uni-directional gravity in suitably scaled variables. This paper proposes analyzes generalization Whitham's to unidirectional nonlinear wave equations consisting general fu...

The interaction and propagation of optical pulses in a nonlinear waveguide array is described by the discrete nonlinear Schrödinger equation i∂zψn = −D(ψn+1 + ψn−1 − 2ψn) − γ|ψn|ψn, (1) whereD is a dispersion (or diffraction) coefficient, and γ is a measure of the nonlinearity. By means of the variational approximation, we study the discrete soliton solutions of this equation. We use a trial fu...

Steady supersonic two-dimensional flows governed by the Navier-Stokes equations are considered. For flows past a thin body, the Oseen theory is shown to fail at large distances. An investigation of the equations bridging the linear and non-linear zones is made. From this, it follows that the resulting equations are a system of Burgers and diffusion equations. The Whitham theory is shown to resu...

Steady, supersonic, dissipative, three-dimensional, axisymmetric flow is considered. A system of Burgers-type equations is shown to govern the flow field. In inviscid regions the Whitham theory gives the limiting form. Dissipative effects ultimately engulf the inviscid zone and at sufficiently large distances from the body the flow is governed by linear dissipative theory. The flow field is div...

Late distributive disambiguation, (3), increases reading measures (first pass, total times, regressions) compared to late collective disambiguation, (4). Early distributive disambiguation, (1), does not significantly increase reading measures compared to early collective disambiguation, (2). Interpretation: Potentially ambiguous predicates are interpreted collectively by the processor ⇒ garden-...