SURFACE SOLITONS IN NONLINEAR ELASTIC MEDIA

We investigate nonlinear surface shear waves in the presence of spatia l dispersion and demonstrate that this dispersion plays a great role i n the structure and modulation stability of nonlinear surface waves. W e show that the possibility of an existence of surface solitons is con nected with the dispersion properties of crystal. Using an asymptotic procedure we found the small amplitude solution for the nonlinear surf ace waves as a power series with the expansion parameter (omega(k)-ome ga)/chi k(2), where omega(k)={k(2) + chi k(4)}(1/2) is the dispersion law of linear waves. In the dispersive media with ''focusing'' nonline arity the nonlinear surface shear waves are modulationally stable in t he case chi<0. But for chi>0 these waves are modulationally unstable a nd give rise to the elastic surface solitons, localized in the plane o f the surface. The amplitude of this envelope soliton is proportional to the value {omega(k)-omega}(1/2)/k(2), its velocity is dose to the g roup velocity of phonons with the same wave number, the region of loca lization near the surface is of the order {omega(k)-omega}(-1/2) and t he size of the localization region in the surface plane is k chi(1/2){ omega(k)-omega}(-1/2). Hence, the surface solitons exist only in the e lastic media with the positive dispersion (d(2) omega/dk(2)>0).