Nonlinear surface waves and solitons
Université Pierre et Marie Curie (Paris 6), Institut Jean Le Rond d'Alembert, UMR CNRS 7190, Case 162, 4 place Jussieu, 75252 Paris Cedex 05, France
First a general introduction on the notion of surface waves on solids (types of different waves), a reminder on the simplest familiar nonlinear dispersive model equations, and another on the basic equations of nonlinear elasticity are given. Then attention is focused on the linear surface wave problem. The main properties of nonlinear surface waves in the absence of dispersion are studied next by use of several asymptotic techniques. The additional effects of dispersion are then considered and combined with those of nonlinearity with an emphasis on the case of so-called shear-horizontal surface waves and solitary-wave solutions for envelope signals. Finally, typical nonlocality is introduced for nonlinear Rayleigh surface waves, and general comments on more general two-dimensional (in propagation space) nonlinear strain waves on structures are evoked by way of conclusion.
© EDP Sciences, Springer-Verlag, 2007