Linear stability theory of solitary waves arising from Hamiltonian systems with symmetry

Stubbe, Joachim

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The aim of this note is to give a short review of our recent work (see []) with Miguel A. Alejo and Luis Vega, concerning the $L^{2}$ -stability, and asymptotic stability, of the $N$ - of the Korteweg-de Vries (KdV) equation.

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Hakkaev, Sevdzhan (2003)

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2000 Mathematics Subject Classification: 35B35, 35B40, 35Q35, 76B25, 76E30. This paper concerns the orbital stability and instability of solitary waves of the system of coupling equations of Benjamin-Bona-Mahony type. By applying the abstract results of Grillakis, Shatah and Strauss and detailed spectral analysis, we obtain the existence and stability of the solitary waves. Partially Supported by Grant MM-810/98 of MESC and by Scientefic Research Grant 19/12.03.2003...

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Partial differential equations endowed with a Hamiltonian structure, like the Korteweg–de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for these waves is still in its infancy though. The issue has been tackled by various means. Of course, it is always possible to address stability from the spectral point of view. However, the link with nonlinear stability - in fact, stability, since...

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