Benzoni-Gavage S.
Weakly nonlinear surface waves
In scale invariant boundary value problems, linear surface waves of finite energy like the Rayleigh waves in elasticity are associated with modulated waves in the weakly nonlinear regime, which are governed by an amplitude equation that is a nonlocal generalization of Burgers' equation. In this talk, we will make the connection between the structure and stability properties of the amplitude equation and those of the original, fully nonlinear problem. We will consider two types of problems: first-order hyperbolic systems of PDEs and higher-order Hamiltonian PDEs, the prototypes of which are the Euler equations of gaz dynamics and the equations of elastodynamics. This is a joint work with Jean-François Coulombel.
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