Perturbation method for a nonlinear wave modulation. III

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Abstract
The perturbation method for the nonlinear, slow modulation of a rapidly oscillatory plane wave, which was given in the first paper of this series for a class of systems of nonlinear partial differential equations, is now established for a general system of nonlinear integro‐partial differential equations. It is shown that the system can be reduced to simpler nonlinear equations which in certain cases become the nonlinear Schrödinger equation. The reduction proceeds as in the first paper, and the result is then applied to nonlinear optics.