On Linearized Korteweg-de Vries Equations

Alfredo Villanueva

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 in  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.


Full Text: PDF DOI: 10.5539/jmr.v4n1p2

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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