Solitary waves in massive nonlinear -sigma models.
Solitons on pseudo-Riemannian manifolds: Stability and motion.
Solutions explosives exceptionnelles
Stability and Instability of Solitary Wave Solutions of a Nonlinear Dispersive System of Benjamin-Bona-Mahony Type
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 of Shumen University.
Stability of periodic waves in Hamiltonian PDEs
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, orbital stability, since we are...
Stability of solitary wave solutions for equations of short and long dispersive waves.