Glimpses of soliton theory : the algebra and geometry of nonlinear PDEs
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The work Glimpses of soliton theory : the algebra and geometry of nonlinear PDEs represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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Glimpses of soliton theory : the algebra and geometry of nonlinear PDEs
Resource Information
The work Glimpses of soliton theory : the algebra and geometry of nonlinear PDEs represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Glimpses of soliton theory : the algebra and geometry of nonlinear PDEs
 Title remainder
 the algebra and geometry of nonlinear PDEs
 Statement of responsibility
 Alex Kasman
 Language
 eng
 Summary

 Solitons are explicit solutions to nonlinear partial differential equations exhibiting particlelike behavior. This is quite surprising, both mathematically and physically. Waves with these properties were once believed to be impossible by leading mathematical physicists, yet they are now not only accepted as a theoretical possibility but are regularly observed in nature and form the basis of modern fiberoptic communication networks. 
 Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last halfcentury. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebrogeometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. 
 Assuming only multivariable calculus and linear algebra as prerequisites, this book introduces the reader to the KdV Equation and its multisoliton solutions, elliptic curves and Weierstrass functions, the algebra of differential operators, Lax Pairs and their use in discovering other soliton equations, wedge products and decomposability, the KP Equation 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 this advanced subject accessible to any undergraduate math major, numerous worked examples and thoughtprovoking but not overlydifficult exercises, footnotes and lists of suggested readings to guide the interested reader to more information, and use of the software package Mathematica± to facilitate computation and to animate the solutions under study. This book provides the reader with a unique glimpse of the unity of mathematics and could form the basis for a selfstudy, onesemester special topics, or "capstone" course. Book Jacket
 Cataloging source
 DLC
 Dewey number
 515/.353
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA377
 LC item number
 .K367 2010
 Literary form
 non fiction
 Nature of contents
 bibliography
 Series statement
 Student mathematical library
 Series volume
 v. 54
Context
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