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On Linearized Korteweg-de Vries Equations

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Author(s): Alfredo Villanueva

Journal: Journal of Mathematics Research
ISSN 1916-9795

Volume: 4;
Issue: 1;
Date: 2012;
Original page

ABSTRACT
Korteweg-de Vries equations (KdV) provide a way of modeling waves on shallow water surfaces. These equations, begun by John Scott Russell in 1834 through observation and experiment, are a type of nonlinear differential equations. Originating with constant coefficients, they now include time-dependent coefficients, modeling ion-acoustic waves inĀ  plasma and acoustic waves on a crystal lattice, and there is even a connection with the Fermi-Pasta-Ulam problem. Most of the solutions are given by solitons or by numerical approximations. In this work we study a linearized KdV equation with time-dependent coefficients (including fifth-order KdV) by using a special ansatz substitution.

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Tangokurs Rapperswil-Jona

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