A hyperbolic generalized Zener model for nonlinear viscoelastic waves

Nonlinear Hyperbolic Surface Waves

We describe examples of hyperbolic surface waves and discuss their connection with initial boundary value and discontinuity problems for hyperbolic systems of PDEs that are weakly but not uniformly stable.

Nonlinear Waves on 3d Hyperbolic Space

In this article, global-in-time dispersive estimates and Strichartz estimates are explored for the wave equation on three dimensional hyperbolic space. Due to the negative curvature, extra dispersion is noted, as compared to the Euclidean case, and a wider range of Strichartz estimates are proved. Using these, small data global existence to semilinear wave equations is shown for a range of powe...

A nonlinear Landau-Zener formula

We consider a system of two coupled ordinary differential equations which appears as an envelope equation in Bose–Einstein Condensation. This system can be viewed as a nonlinear extension of the celebrated model introduced by Landau and Zener. We show how the nonlinear system may appear from different physical models. We focus our attention on the large time behavior of the solution. We show th...

Nonlinear Asymptotics for Hyperbolic Internal Waves of Small Width

In the limit ε → 0, the solutions converge to piecewise smooth functions which are discontinuous accross a characteristic surface. Such solutions have source terms which are also piecewise smooth. Discontinuous sources are idealizations of smooth sources with a thin (∼ ε) transition layer. The fundamental problem addressed here is to describe the dynamics of solutions with sources with such tra...

On Nonlinear Water Waves in a Channel