Super compact equation for water waves

Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...

On a fourth-order envelope equation for deep-water waves

The ordinary nonlinear Schrodinger equation for deep-water waves (found by a perturbation analysis to 0(€3 ) in the wave steepness €) compares unfavourably with the exact calculations of Longuet-Higgins (1978) for € > 0·10. Dysthe (1979) showed that a significant improvement is found by taking the perturbation analysis one step further to 0(€ ). One of the dominant new effects is the wave-induc...

Global Solutions for the Gravity Water Waves Equation in Dimension

We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L related norms, with dispersive estimates, which give decay in L∞. To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.

Numerical Solution of Parabolized Stability Equations Using Super Compact Scheme

A SUPER ZERO-REST-MASS-EQUATION

Various authors have considered the Zero-rest-mass equation and the contour integral representation of its solutions. Ferber generalized these equations to supertwistor spaces with 2N odd components so that with N=O we get the standard ungraded twistors of Penrose. In this paper we use the Batchelor theorem toconstruct the natural super Twistor space with coarse topology with underlying sta...