The DOI matches its Crossref record; 55 of the 55 references it cites were found in a registry or an index.
Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons
Abstract
The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.
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(2020) · Electromagnetic Processes · doi:10.2307/j.ctv131bv37.5 · Cited by 21,966
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An Introduction to Fluid Dynamics
Batchelor, G. K. (2000) · doi:10.1017/cbo9780511800955 · Cited by 12,360
Electrodynamics of Continuous Media
Landau, L. D., Lifshitz, E. M., & King, A. L. (1961) · American Journal of Physics · doi:10.1119/1.1937882 · Cited by 10,997
Goldstein, H. (1951) · UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno · Cited by 10,004
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Finite Volume Methods for Hyperbolic Problems
LeVeque, R. J. (2002) · Cambridge University Press eBooks · doi:10.1017/cbo9780511791253 · Cited by 6,313
Solitons, Nonlinear Evolution Equations and Inverse Scattering
Ablowitz, M. A., & Clarkson, P. A. (1991) · Cambridge University Press eBooks · doi:10.1017/cbo9780511623998 · Cited by 6,109
Self-citationAdvanced Mathematical Methods for Scientists and Engineers I
Bender, C. M., & Orszag, S. A. (1999) · doi:10.1007/978-1-4757-3069-2 · Cited by 4,906
Solitons and the Inverse Scattering Transform
Ablowitz, M. J., & Segur, H. (1981) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611970883 · Cited by 4,870
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Jagtap, A. D., Kharazmi, E., & Karniadakis, G. E. (2020) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2020.113028 · Cited by 1,208
Higher Order Dynamic Mode Decomposition
Le Clainche, S., & Vega, J. M. (2017) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/15m1054924 · Cited by 417
Gulevich, D. R., Yudin, D., Skryabin, D. V., Iorsh, I. V., & Shelykh, I. A. (2017) · Scientific Reports · doi:10.1038/s41598-017-01646-y · Cited by 87
Metadata
- Authors
- Ablowitz, M. J.
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 2011-09-08
- OpenAlex
- W630319947
- Cited by
- 443
- References
- 55
- FWCI
- 3.52
- Type
- book
- Language
- en
- Open access
- closed
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