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The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
Abstract
A systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering. The form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro‐differential operator. A comprehensive presentation of the inverse scattering method is given and general features of the solution are discussed. The relationship of the scattering theory and Backlund transformations is brought out. In view of the role of the dispersion relation, the comparatively simple asymptotic states, and the similarity of the method itself to Fourier transforms, this theory can be considered a natural extension of Fourier analysis to nonlinear problems.
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Cited by
Lederer, F., Stegeman, G. I., Christodoulides, D. N., Assanto, G., Segev, M., & Silberberg, Y. (2008) · Physics Reports · doi:10.1016/j.physrep.2008.04.004 · Cited by 1,180
Currie, J. F., Krumhansl, J. A., Bishop, A. R., & Trullinger, S. E. (1980) · Physical Review B · doi:10.1103/physrevb.22.477 · Cited by 517
Blanco-Redondo, A., de Sterke, C. M., Sipe, J. E., Krauss, T. F., Eggleton, B. J., & Husko, C. (2016) · Nature Communications · doi:10.1038/ncomms10427 · Cited by 285
Metadata
- Authors
- Ablowitz, M. J., Kaup, D. J., Newell, A. C., & Segur, H.
- Venue
- Studies in Applied Mathematics
- Publisher
- Wiley
- Published
- 1974-12
- Volume
- 53
- Issue
- 4
- Pages
- 249-315
- ISSN
- 0022-2526 (ISSN-L)
- 1467-9590
- OpenAlex
- W1631607997
- Cited by
- 3,187
- References
- 0
- FWCI
- 56.63
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems. https://app.cochat.ai/papers/10.1002/sapm1974534249
- The paper
- Ablowitz, M. J., Kaup, D. J., Newell, A. C., & Segur, H. (1974). The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems. Studies in Applied Mathematics. https://doi.org/10.1002/sapm1974534249
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
