BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Stability of periodic travelling wave solutions to Korteweg-de Vries and related equations Trichtchenko, Olga


In this talk, we explore the simplest equation that exhibits high frequency instabilities, the fifth-order Korteweg-de Vries equation. We show how to derive the necessary condition for an instability of a perturbation of a small amplitude, periodic travelling wave solutions. We proceed by examining how these unstable perturbations change and grow in time as the underlying solution changes. We conclude by commenting on what happens with a different nonlinearity in the underlying equation.

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