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Nonlinear instability of a critical traveling wave in the generalized Korteweg -- de Vries equation

Andrew Comech·Scipio Cuccagna·Dmitry Pelinovsky
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Abstract

We prove the instability of a ``critical'' solitary wave of the generalized Korteweg -- de Vries equation, the one with the speed at the border between the stability and instability regions. The instability mechanism involved is ``purely nonlinear'', in the sense that the linearization at a critical soliton does not have eigenvalues with positive real part. We prove that critical solitons correspond generally to the saddle-node bifurcation of two branches of solitons.

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Andrew Comech, Scipio Cuccagna, Dmitry Pelinovsky. 2006-09-01. Nonlinear instability of a critical traveling wave in the generalized Korteweg -- de Vries equation. https://arxiv.org/abs/math/0609010

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