Zero-dispersion Limit Research Articles

On a nonlinear hyperbolic variational equation: II. The zero-viscosity and dispersion limits

We consider viscosity and dispersion regularizations of the nonlinear hyperbolic partial differential equation (u t+uux)x=1/2u x 2 with the simplest initial data such that u x blows up in finite time. We prove that the zero-viscosity limit selects a unique global weak solution of the partial differential equation without viscosity. We also present numerical experiments which indicate that the zero-dispersion limit selects a different global weak solution of the same initial-value problem.

Hydrodynamical reductions of the lattice KP hierarchy

Hydrodynamic reductions are found for the lattice KP hierarchy and its zero-dispersion limit. This is similar to the continuous case where the reductions result in dispersive water waves and Benney hierarchies respectively.