NONLINEAR WAVE PROPAGATION IN THE GEOMETRICAL APPROXIMATION.
BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS
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A geometrical theory of nonlinear wave propagation is developed for a class of stationary principles which includes some models of nonlinear optics. The geometrical approximation differs from the Quasi-optical approximation in a number of ways, including the fact that it can be shown to be the first of a rational sequence of approximations. The geometrical approximation is derived here in one of several ways it might have been introduced, and a number of its predictions are worked out in detail. Stability of a nonlinear beam, qualitative aspects of its propagation in the steady state, and specific examples that illustrate the effect of different kinds of nonlinearity are discussed. Finally, a nonlinear stationary principle for electromagnetic theory is proposed, and the qualitative features of the corresponding geometrical nonlinear optics are discussed. Author