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Perturbation Method for a Nonlinear Wave Modulation. I
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.
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Citations
Cited by
Molecular-dynamics study of a three-dimensional one-component model for distortive phase transitions
Schneider, T., & Stoll, E. (1978) · Physical Review B · doi:10.1103/physrevb.17.1302 · Cited by 1,592
Blow-up in Nonlinear Schroedinger Equations-I A General Review
Rasmussen, J. J., & Rypdal, K. (1986) · Physica Scripta · doi:10.1088/0031-8949/33/6/001 · Cited by 447
Models of few optical cycle solitons beyond the slowly varying envelope approximation
Leblond, H., & Mihalache, D. (2013) · Physics Reports · doi:10.1016/j.physrep.2012.10.006 · Cited by 431
Metadata
- Authors
- Taniuti, T., & Yajima, N.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1969-08-01
- Volume
- 10
- Issue
- 8
- Pages
- 1369-1372
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W4246128427
- Cited by
- 541
- References
- 0
- FWCI
- 15.68
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Perturbation Method for a Nonlinear Wave Modulation. I. https://app.cochat.ai/papers/10.1063/1.1664975
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- Taniuti, T., & Yajima, N. (1969). Perturbation Method for a Nonlinear Wave Modulation. I. Journal of Mathematical Physics. https://doi.org/10.1063/1.1664975
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