Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons (Cambridge Texts in Applied Mathematics Book 47) 1st Edition by Mark J. Ablowitz (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book isn’t really gentle, as much as his book in complex analysis appears to be. In fact, his book on Complex Analysis is almost too detailed, a bit verbose in the mathematics. This one however is quite concise and skips a lot of details, assuming you know quite a bit or just deriving the mathematics a bit too fast. This is some deep stuff here, dispersive equations are no joke. By the look of his website, this man is an expert on these, but this book fails to present the subject matter in a manner that is elementary, say to the student who has studied some basic analysis, diffferential equations, and Fourier Series. Not saying it’s impossible for this kind of student to approach it, but it’s not gentle reading and to have the trust that the author is leading you to somewhere nice with this kind of effort and depth is hard without a better motivation than he gives at the beginning, which is limited to some very specific differential equations without a very broad view in relation to the overall mathematics he seeks to develop. For this reason, I have preferred the Debnath Nonlinear Equations I am waiting for arrival to review. I am familiar with his text as I have seen it in the library, and it is a bit more down to Earth, though not quite as specific on the subject matter Ablowitz addresses here, they do contain related and sometimes identical mathematics and Debnath is certainly more gentlemanly and kind in guiding you through the quite intricate mathematics involved in nonlinear wave equations.

⭐Very specialist, but that’s what you expect from the title.

⭐Ok.

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