Glimpses of Soliton Theory (Student Mathematical Library, 100)
Language: English
Published by American Mathematical Society, 2023
- Softcover
- Used
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- Title
- Glimpses of Soliton Theory (Student Mathematical Library, 100)
- Author
- Alex Kasman
- Publisher
- American Mathematical Society
- Publication year
- 2023
- Condition
- Good
- Binding
- paperback
- Language
- English
- ISBN 10
- 1470472627
- ISBN 13
- 9781470472627
- Edition
- 2nd Edition.
Glimpses of Soliton Theory reveals the hidden connections discovered over the last half-century that explain the existence of these mysterious mathematical objects. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant explanation of something seemingly miraculous.
Assuming only multivariable calculus and linear algebra, the book introduces the reader to the KdV Equation and its multisoliton solutions, elliptic curves and Weierstrass $\wp$-functions, the algebra of differential operators, Lax Pairs and their use in discovering other soliton equations, wedge products and decomposability, the KP Hierarchy, and Sato's theory relating the Bilinear KP Equation to the geometry of Grassmannians.
Notable features of the book include: careful selection of topics and detailed explanations to make the subject accessible to undergraduates, numerous worked examples and thought-provoking exercises, footnotes and lists of suggested readings to guide the interested reader to more information, and use of MathematicaR to facilitate computation and animate solutions.
The second edition refines the exposition in every chapter, adds more homework exercises and projects, updates references, and includes new examples involving non-commutative integrable systems. Moreover, the chapter on KdV multisolitons has been greatly expanded with new theorems providing a thorough analysis of their behavior and decomposition.
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