Abstract
By extending the asymptotic method of G. E. Kuzmak, J. C. Luke has shown how G. B. Whitham’s theory of nonlinear wave propagation can be derived directly from the partial differential equation without using the variational principle, in special cases. We apply the same method to a more general class of nonlinear second order partial differential equations or systems of first order equations containing a small parameter e and obtain asymptotic expansions of the solutions.
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