Place: Institut Henri Poincaré, 11 rue Pierre et Marie Curie, F-75005 Paris, France Local: 421 Time: 15:45
Abstract: The science of nonlinear dispersive waves was born at the end of the 19th century, when the first asymptotic water-wave models were derived by Boussinesq and later on by Korteweg and de Vries to explain the propagation of waves observed some decades earlier by the naval engineer John Scott Russell. Those models turned out in the 20th century to have analogs in several fields of mathematical physics in which dissipative phenomena are negligible while wave propagation is nonlinear and subject to dispersion. Applications range indeed from water waves to superfluids and nonlinear optics. The mathematical theory of nonlinear dispersive partial differential equations (PDE) still conceals tough open questions. The talk will address a few topics regarding qualitative properties of such PDEs, and more specifically the stability of travelling wave solutions.
Related publications: S. Benzoni-Gavage, C. Mietka, and L. M. Rodrigues. Stability of periodic waves in Hamiltonian PDEs of either long wavelength or small amplitude. Indiana Univ. Math. J., to appear. preprint hal-01590731. S. Benzoni-Gavage, C. Mietka, and L. M. Rodrigues. Co-periodic stability of periodic waves in some Hamiltonian PDEs. Nonlinearity, 29(11):3241, 2016.
PDEs, nonlinear dispersive waves, water waves, superfluids, nonlinear optics
Interdisciplinary European Academy of Sciences - Académie Européenne Interdisciplinaire des Sciences