Zobrazeno 1 - 10
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pro vyhledávání: '"Ketcheson, David"'
We study the recently-proposed hyperbolic approximation of the Korteweg-de Vries equation (KdV). We show that this approximation, which we call KdVH, possesses a rich variety of solutions, including solitary wave solutions that approximate KdV solito
Externí odkaz:
http://arxiv.org/abs/2412.17117
Autor:
Ketcheson, David I., Russo, Giovanni
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 show through asymptotic analysis that long-wavelength perturbations appro
Externí odkaz:
http://arxiv.org/abs/2412.11086
Autor:
Busaleh, Laila S., Ketcheson, David I.
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 effective equations, which take the form of a constant-coefficient system of
Externí odkaz:
http://arxiv.org/abs/2410.05176
Autor:
Ketcheson, David I., Russo, Giovanni
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 constant direction are known to evolve into solitary waves, due to an eff
Externí odkaz:
http://arxiv.org/abs/2409.00076
Using a recent characterization of energy-preserving B-series, we derive the explicit conditions on the coefficients of a Runge-Kutta method that ensure energy preservation (for Hamiltonian systems) up to a given order in the step size, which we refe
Externí odkaz:
http://arxiv.org/abs/2407.15365
Autor:
Ketcheson, David I., Biswas, Abhijit
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 have received increasing interest in recent years, and are potentially u
Externí odkaz:
http://arxiv.org/abs/2405.16841
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 known to generally exhibit wave breaking, numerical experiments sugge
Externí odkaz:
http://arxiv.org/abs/2311.02603
Explicit Runge--Kutta (RK) methods are susceptible to a reduction in the observed order of convergence when applied to initial-boundary value problem with time-dependent boundary conditions. We study conditions on explicit RK methods that guarantee h
Externí odkaz:
http://arxiv.org/abs/2310.02817
Autor:
Biswas, Abhijit, Ketcheson, David I.
The nonlinear Schr\"{o}dinger (NLS) equation possesses an infinite hierarchy of conserved densities and the numerical preservation of some of these quantities is critical for accurate long-time simulations, particularly for multi-soliton solutions. W
Externí odkaz:
http://arxiv.org/abs/2309.02324
We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately resolve fine s
Externí odkaz:
http://arxiv.org/abs/2307.11842