Perturbation Method for a Nonlinear Wave Modulation. I
- 1 August 1969
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 10 (8) , 1369-1372
- https://doi.org/10.1063/1.1664975
Abstract
In this paper we consider a system of nonlinear wave equations which admits, in a linear approximation, a planewave solution with high‐frequency oscillation. Then, for the wave of small but finite amplitude, we investigate how slowly varying parts of the wave such as the amplitude are modulated by nonlinear self‐interactions. A stretching transformation shows that, in the lowest order of an asymptotic expansion, the original system of equations can be reduced to a tractable, single, nonlinear equation to determine the amplitude modulation.Keywords
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