6 papers · 1 filter
Solitary wave formation in the compressible Euler equations
David I. Ketcheson, Giovanni Russo
We study the behavior of perturbations in a compressible one-dimensional inviscid gas with an ambient state consisting of constant pressure and periodically-varying density. We sho…
Homogenized Equations for Isentropic Gas in a Pipe with Periodically-Varying Cross-Section
Laila S. Busaleh, David I. Ketcheson
We analyze the behavior of an isentropic gas in a narrow pipe with periodically-varying cross-sectional area. Using multiple-scale perturbation theory, we derive homogenized effect…
A Hyperbolic Approximation of the Nonlinear Schrödinger Equation
Abhijit Biswas, Laila S. Busaleh, David I. Ketcheson +2
We study a first-order hyperbolic approximation of the nonlinear Schrödinger (NLS) equation. We show that the system is strictly hyperbolic and possesses a modified Hamiltonian st…
A dispersive effective equation for transverse propagation of planar shallow water waves over periodic bathymetry
David I. Ketcheson, Giovanni Russo
We study the behavior of shallow water waves propagating over bathymetry that varies periodically in one direction and is constant in the other. Plane waves traveling along the con…
Approximation of arbitrarily high-order PDEs by first-order hyperbolic relaxation
David I. Ketcheson, Abhijit Biswas
We present a framework for constructing a first-order hyperbolic system whose solution approximates that of a desired higher-order evolution equation. Constructions of this kind ha…
A multiscale model for weakly nonlinear shallow water waves over periodic bathymetry
David I. Ketcheson, Lajos Lóczi, Giovanni Russo
We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are…