Stability of nonlinear waves

A numerical study of the spatial evolution of the transverse distribution of the field of a surface wave, propagating at an interface between two dielectrics, is presented, covering the 2-dimensional case in which the field does not depend on the coordinate y, and the solution is obtained in the form of a wave propagating along the x-axis with a slowly varying amplitude. Among the inferences made one is that the surface wave of the unstable branch can be excited by a light beam of optimum shape and given power which is incident on the boundary of a nonlinear medium at an angle greater than the critical angle for total internal reflection.