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Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear PDEs (Student Mathematical Library, 100) - Softcover
Inhaltsangabe
"By covering a carefully selected subset of topics, offering detailed explanations and examples, and with the occasional assistance of technology, this book aims to introduce undergraduate students to a subject normally only encountered by graduate students and researchers. Because of its interdisciplinary nature (bringing together different branches of mathematics as well as having connections to science and engineering), it is hoped that this book would be ideal for a one semester special topics class,"capstone" or reading course."--
Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.
Über die Autorin bzw. den Autor
Alex Kasman, College of Charleston, SC.
„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.
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Student Mathematical Library - 100: Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear PDEs, Second Edition
Verlag:
American Mathematical Society, 2023
ISBN 10: 1470472627
ISBN 13: 9781470472627
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Softcover. Zustand: As New. 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. Bestandsnummer des Verkäufers 9bade4f4-7c09-46c3-aef5-353085abc6e1
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Glimpses of Soliton Theory (Student Mathematical Library, 100)
Verlag:
American Mathematical Society, 2023
ISBN 10: 1470472627
ISBN 13: 9781470472627
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paperback. Zustand: Good. 2nd Edition. Ships in a BOX from Central Missouri! May not include working access code. Will not include dust jacket. Has used sticker(s) and some writing or highlighting. UPS shipping for most packages, (Priority Mail for AK/HI/APO/PO Boxes). Bestandsnummer des Verkäufers 011089637U
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Glimpses of Soliton Theory : The Algebra and Geometry of Nonlinear PDEs
Verlag:
American Mathematical Society, 2023
ISBN 10: 1470472627
ISBN 13: 9781470472627
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Zustand: good. May show signs of wear, highlighting, writing, and previous use. This item may be a former library book with typical markings. No guarantee on products that contain supplements Your satisfaction is 100% guaranteed. Twenty-five year bookseller with shipments to over fifty million happy customers. Bestandsnummer des Verkäufers 45772272-5
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Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear PDEs (eng)
Verlag:
American Mathematical Society, 2023
ISBN 10: 1470472627
ISBN 13: 9781470472627
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Glimpses of Soliton Theory
Verlag:
American Mathematical Society, US, 2023
ISBN 10: 1470472627
ISBN 13: 9781470472627
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Paperback. Zustand: New. Second Edition. Solitons are nonlinear waves which behave like interacting particles. When first proposed in the 19th century, leading mathematical physicists denied that such a thing could exist. Now they are regularly observed in nature, shedding light on phenomena like rogue waves and DNA transcription. Solitons of light are even used by engineers for data transmission and optical switches. Furthermore, unlike most nonlinear partial differential equations, soliton equations have the remarkable property of being exactly solvable. Explicit solutions to those equations provide a rare window into what is possible in the realm of nonlinearity.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. Bestandsnummer des Verkäufers LU-9781470472627
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Glimpses of Soliton Theory : The Algebra and Geometry of Nonlinear PDEs
Verlag:
American Mathematical Society, 2023
ISBN 10: 1470472627
ISBN 13: 9781470472627
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Softcover
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Zustand: good. May show signs of wear, highlighting, writing, and previous use. This item may be a former library book with typical markings. No guarantee on products that contain supplements Your satisfaction is 100% guaranteed. Twenty-five year bookseller with shipments to over fifty million happy customers. Bestandsnummer des Verkäufers 45772272-5
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Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear PDEs
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ISBN 10: 1470472627
ISBN 13: 9781470472627
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Zustand: New. 2023. 2nd Edition. paperback. . . . . . Bestandsnummer des Verkäufers V9781470472627
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Glimpses of Soliton Theory
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Glimpses of Soliton Theory : The Algebra and Geometry of Nonlinear PDEs
Verlag:
American Mathematical Society, 2023
ISBN 10: 1470472627
ISBN 13: 9781470472627
Neu
Softcover
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Glimpses of Soliton Theory (Paperback)
Verlag:
American Mathematical Society, Providence, 2023
ISBN 10: 1470472627
ISBN 13: 9781470472627
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Paperback. Zustand: new. Paperback. Solitons are nonlinear waves which behave like interacting particles. When first proposed in the 19th century, leading mathematical physicists denied that such a thing could exist. Now they are regularly observed in nature, shedding light on phenomena like rogue waves and DNA transcription. Solitons of light are even used by engineers for data transmission and optical switches. Furthermore, unlike most nonlinear partial differential equations, soliton equations have the remarkable property of being exactly solvable. Explicit solutions to those equations provide a rare window into what is possible in the realm of nonlinearity.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. Reveals the hidden connections discovered over the last half-century that explain the existence of these mysterious mathematical objects. The book aims to convince the reader that the underlying algebro-geometric structure of soliton equations provides an elegant explanation of something seemingly miraculous. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9781470472627