19 citations · 44 across the 6 of their papers we have counts for
6 papers
Waves in Strongly Nonlinear Gardner-like Equations on a Lattice
Philip Rosenau, Arkady Pikovsky
We introduce and study a family of lattice equations which may be viewed either as a strongly nonlinear discrete extension of the Gardner equation, or a non-convex variant of the L…
Flatons: flat-top solitons in extended Gardner equations
Philip Rosenau, Alexander Oron
In both the Gardner equation and its extensions, the non-convex convection bounds the range of solitons / compactons velocities beyond which they dissolve and kink/anti-kink form.…
Solitary phase waves in a chain of autonomous oscillators
Philip Rosenau, Arkady Pikovsky
In the present paper we study phase waves of self-sustained oscillators with a nearest neighbor dispersive coupling on an infinite lattice. To analyze the underlying dynamics we ap…
Loss of Regularity in the Equations
Alon Zilburg, Philip Rosenau
Using a priori estimates we prove that initially nonnegative, smooth and compactly supported solutions of the equations must lose their smoothness in finite time. Formatio…
A subluminous Schroedinger equation
Philip Rosenau, Zeev Schuss
The standard derivation of Schroedinger's equation from a Lorentz-invariant Feynman path integral consists in taking first the limit of infinite speed of light and then the limit o…
On a Hamiltonian PDE arising in Magma Dynamics
Gideon Simpson, Michael I. Weinstein, Philip Rosenau
In this article we discuss a new Hamiltonian PDE arising from a class of equations appearing in the study of magma, partially molten rock, in the Earth's interior. Under physically…