The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
Displaying 81 –
100 of
165
We deal with numerical analysis and simulations of the Davey-Stewartson equations which model, for example, the evolution of water surface waves. This time dependent PDE system is particularly interesting as a generalization of the 1-d integrable NLS to 2 space dimensions. We use a time splitting spectral method where we give a convergence analysis for the semi-discrete version of the scheme. Numerical results are presented for various blow-up phenomena of the equation, including blowup of defocusing,...
We deal with numerical analysis and simulations of the Davey-Stewartson equations
which model, for example, the evolution of water surface waves.
This time dependent PDE system is particularly interesting as a generalization
of the 1-d integrable NLS to 2 space dimensions.
We use a time splitting spectral method where
we give a convergence analysis for the semi-discrete version of the scheme.
Numerical results are presented for various blow-up phenomena of
the equation, including blowup of defocusing,...
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...
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...
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...
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...
Currently displaying 81 –
100 of
165