Format:
1 Online-Ressource (xiv, 348 pages)
,
digital, PDF file(s)
ISBN:
9780511998324
Series Statement:
Cambridge texts in applied mathematics 47
Content:
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
Content:
Machine generated contents note: Preface; Acknowledgements; Part I. Fundamentals and Basic Applications: 1. Introduction; 2. Linear and nonlinear wave equations; 3. Asymptotic analysis of wave equations; 4. Perturbation analysis; 5. Water waves and KdV type equations; 6. Nonlinear Schrödinger models and water waves; 7. Nonlinear Schrödinger models in nonlinear optics; Part II. Integrability and Solitons: 8. Solitons and integrable equations; 9. Inverse scattering transform for the KdV equation; Part III. Novel Applications of Nonlinear Waves: 10. Communications; 11. Mode-locked lasers; 12. Nonlinear photonic lattices; References; Index
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Additional Edition:
ISBN 9781107012547
Additional Edition:
ISBN 9781107664104
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9781107012547
Language:
English
DOI:
10.1017/CBO9780511998324
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