Student Mathematical Library - 100: Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear PDEs, Second Edition
Language: English
Published by American Mathematical Society, 2023
- Softcover
- Used
Condition: Used - As new
£ 12.05
Quantity: 1 available
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Originalverpackt. This book challenges and intrigues from beginning to end, making it ideal for a capstone course or senior seminar. Solitons, nonlinear waves that behave like interacting particles, were initially dismissed by leading mathematical physicists in the 19th century. Today, they are observed in nature, illuminating phenomena such as rogue waves and DNA transcription. Engineers utilize solitons of light for data transmission and optical switches. Unlike most nonlinear partial differential equations, soliton equations are exactly solvable, offering explicit solutions that reveal the possibilities within nonlinearity. The text explores the connections uncovered over the last fifty years that elucidate these mathematical objects, presenting the algebro-geometric structure of soliton equations as a sophisticated explanation for their existence. The book introduces the KdV Equation and its multisoliton solutions, elliptic curves, differential operators, Lax Pairs, the KP Hierarchy, and Sato's theory linking the Bilinear KP Equation to Grassmannian geometry, all while assuming a background in multivariable calculus and linear algebra. Notable features include a careful selection of topics, detailed explanations, numerous examples, thought-provoking exercises, and the use of Mathematica® for computation. The second edition refines the exposition, adds homework exercises, updates references, and expands the chapter on KdV multisolitons with.…
Seller Inventory # 9bade4f4-7c09-46c3-aef5-353085abc6e1
- Title
- Student Mathematical Library - 100: Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear PDEs, Second Edition
- Author
- Alex Kasman
- Publisher
- American Mathematical Society
- Publication year
- 2023
- Condition
- As New
- Binding
- Softcover
- 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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About the Author
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