Asymptotic solutions of nonlinear wave equations using the methods of averaging and two-timing

Lardner, R. W.

doi:10.1090/qam/442443

Author: R. W. Lardner
Journal: Quart. Appl. Math. 35 (1977), 225-238
MSC: Primary 35B25; Secondary 35L20
DOI: https://doi.org/10.1090/qam/442443
MathSciNet review: 442443
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Abstract: The method of averaging and the two-time procedure are outlined for a class of hyperbolic second-order partial differential equations with small nonlinearities. It is shown that they both lead to the same integro-differential equation for the lowest-order approximation to the solution. For the special case of the nonlinear wave equation, this lowest-order solution consists of the superposition of two modulated travelling waves, and separate integro-differential equations are derived for the amplitudes of these two waves. As an example, the wave equation with Van der Pol type of nonlinearity is considered.

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