Oblique interface-wave diffraction by a small bottom deformation in two superposed fluids.
On a model system for the oblique interaction of internal gravity waves
On a model system for the oblique interaction of internal gravity waves
We give local and global well-posedness results for a system of two Kadomtsev-Petviashvili (KP) equations derived by R. Grimshaw and Y. Zhu to model the oblique interaction of weakly nonlinear, two dimensional, long internal waves in shallow fluids. We also prove a smoothing effect for the amplitudes of the interacting waves. We use the Fourier transform restriction norms introduced by J. Bourgain and the Strichartz estimates for the linear KP group. Finally we extend the result of [3] for lower...
On a non-homogeneous shallow-water problem
On a nonlinear convolution equation occurring in the theory of water percolation
On a problem of shallow water type.
On a singular integral equation with log kernel and its application.
On Composite Mesh Difference Methods for Hyperbolic Differential Equations.
On generation and propagation of tsunamis in a shallow running ocean.
On oblique waves forcing by a porous cylindrical wall.
On permanent capillar-heavy waves of two liquids flowing one upon the other
On singularities of capillary surfaces in the absence of gravity.
On some Boussinesq systems in two space dimensions: theory and numerical analysis
A three-parameter family of Boussinesq type systems in two space dimensions is considered. These systems approximate the three-dimensional Euler equations, and consist of three nonlinear dispersive wave equations that describe two-way propagation of long surface waves of small amplitude in ideal fluids over a horizontal bottom. For a subset of these systems it is proved that their Cauchy problem is locally well-posed in suitable Sobolev classes. Further, a class of these systems is discretized...
On Strongly Interacting Internal Solitary Waves.
On the complete integrability of an equation having solitons but not known to have a lax pair.
On the computation of roll waves
The phenomenon of roll waves occurs in a uniform open-channel flow down an incline, when the Froude number is above two. The goal of this paper is to analyze the behavior of numerical approximations to a model roll wave equation which arises as a weakly nonlinear approximation of the shallow water equations. The main difficulty associated with the numerical approximation of this problem is its linear instability. Numerical round-off error can easily overtake the numerical solution and yields false...
On the Computation of Roll Waves
The phenomenon of roll waves occurs in a uniform open-channel flow down an incline, when the Froude number is above two. The goal of this paper is to analyze the behavior of numerical approximations to a model roll wave equation ut + uux = u,u(x,0) = u0(x), which arises as a weakly nonlinear approximation of the shallow water equations. The main difficulty associated with the numerical approximation of this problem is its linear instability. Numerical round-off error can easily overtake the...
On the convective nature of roll waves instability.
On the derivation of the nonlinear discrete equations numerically integrating the Euler PDEs.
On the instability of solitary-wave solutions for fifth-order water wave models.