We consider time-independent solutions of hyperbolic equations such as âˆ‚ tt u âˆ’ âˆ†u = f (x, u) where f is convex in u. We prove that linear instability with a positive eigen-function implies nonlinearâ€¦ (More)

We consider the linear stability problem for a symmetric equilibrium of the relativistic Vlasov-Maxwell (RVM) system. For an equilibrium whose distribution function depends monotonically on theâ€¦ (More)

obtained by Fuchssteiner and Fokas [9] by the method of recursion operators, is in dimensionless space-time variables (x, t) a model for the unidirectional propagation of shallow water waves over aâ€¦ (More)

Abstract. We consider the linear stability problem for a 3D cylindrically symmetric equilibrium of the relativistic Vlasov-Maxwell system that describes a collisionless plasma. For an equilibriumâ€¦ (More)

We construct large families of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a flat bed. A Riemann-Hilbert problem approach isâ€¦ (More)

Consider a collisionless relativistic neutral plasma. An oscillatory-tail equilibrium is a state whose magnetic eld connects two different constant states at x = ?1 and x = +1 and whose electric eldâ€¦ (More)

I will consider classical 2D traveling water waves with vorticity. By means of local and global bifurcation theory using topological degree, we now know that there exist many such waves. They areâ€¦ (More)