TY  - BOOK
AU  - Ablowitz,Mark J.
TI  - Nonlinear dispersive waves: asymptotic analysis and solitons 
T2  - Cambridge texts in applied mathematics
SN  - 9780511998324 (ebook)
AV  - QC174.26.W28 A264 2011
U1  - 530.15/5355 23
PY  - 2011///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Wave equation
KW  - Nonlinear waves
KW  - Solitons
KW  - Asymptotic expansions
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015); 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
N2  - 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
UR  - https://doi.org/10.1017/CBO9780511998324
ER  -