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.

Nonlinear instability of a critical traveling wave in the generalized Korteweg -- de Vries equation / Cuccagna, Scipio; Andrew, Comech; Dmitry, Pelinovsky. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - 39:(2007), pp. 1-33.

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

CUCCAGNA, Scipio;
2007

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.
39
1
33
Nonlinear instability of a critical traveling wave in the generalized Korteweg -- de Vries equation / Cuccagna, Scipio; Andrew, Comech; Dmitry, Pelinovsky. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - 39:(2007), pp. 1-33.
Cuccagna, Scipio; Andrew, Comech; Dmitry, Pelinovsky
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/421720
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