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Nonlinear periodic waves and their modulations : : An introductory course / A.M. Kamchatnov

Tác giả : A.M. Kamchatnov

Nhà xuất bản : World Scientific

Năm xuất bản : 2000

Nơi xuất bản : Singapore

Mô tả vật lý : xiv, 383 p. : ill. ; 23 cm

ISBN : 981024407X

Số phân loại : 531.1133

Chủ đề : 1. Chuyển động sóng, Lý thuyết. 2. Sóng phi tuyến. 3. Nonlinear waves. 4. Solitons. 5. Sóng.

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Tóm tắt :

This volume develops the techniques of the theory of nonlinear periodic waves at elementary level and in pedagogical detail. It provides an introduction to a Whitham's theory of modulation in a form suitable for applications. The exposition is based on an analysis of representative examples taken from fluid mechanics, nonlinear optics and plasma physics rather than on the formulation and study of a mathematical theory. Much attention is paid to physical motivations of the mathematical methods developed in the book. The main applications covered include the theory of collisionless shock waves in dispersive systems and the nonlinear theory of soliton formation in modulationally unstable systems. Exercises are provided to amplify the discussion of important topics such as singular perturbation theory, Riemann invariants, the finite gap integration method, and Whitham equations and their solutions.

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