Categories
Download Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear Pdes (Student Mathematical Library)

Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear Pdes (Student Mathematical Library)

  • Author: Alex Kasman
  • Pages: 304
  • Language: English
  • ISBN/ASIN: 0821852450
  • ISBN13: 9780821852453
  • Upload date: 22-12-2016, 17:10
  • Category: Mathematics

Solitons are explicit solutions to nonlinear partial differential equations exhibiting particle-like 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 fiber-optic communication networks. Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. 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 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 $wp$-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 thought-provoking but not overly-difficult exercises, footnotes and lists of suggested readings to guide the interested reader to more information, and use of the software package MathematicaA® 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 self-study, one-semester special topics, or "capstone" course.

Download Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear Pdes (Student Mathematical Library)

* If download links doesn't work. Please write a comment.

Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear Pdes (Student Mathematical Library) Download via usenet

Comments for Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear Pdes (Student Mathematical Library)

Related eBooks

Download Variational Methods in Nonlinear Field Equations: Solitary Waves, Hylomorphic Solitons and VorticesVariational Methods in Nonlinear Field Equations: Solitary Waves, Hylomorphic Solitons and Vortices Vieri Benci Download Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations (Contemporary Mathematics and Its Applications Book Series)Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations (Contemporary Mathematics and Its Applications Book Series) Vicentiu Radulescu Download Partial Differential Equations: An Introduction to Theory and ApplicationsPartial Differential Equations: An Introduction to Theory and Applications Michael Shearer Download Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative AnalysisPartial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis Vicentiu D. Radulescu Download Partial Differential Equations III: Nonlinear EquationsPartial Differential Equations III: Nonlinear Equations Michael Taylor Download Ordinary Differential Equations: Introduction and Qualitative Theory, Third EditionOrdinary Differential Equations: Introduction and Qualitative Theory, Third Edition Jane Cronin Download Nonlinear Partial Differential Equations with Applications (International Series of Numerical Mathematics)Nonlinear Partial Differential Equations with Applications (International Series of Numerical Mathematics) Tomas Roubicek Download Local And Global Analysis of Nonlinear Dispersive And Wave EquationsLocal And Global Analysis of Nonlinear Dispersive And Wave Equations Terence Tao Download Linear Algebra and GeometryLinear Algebra and Geometry Igor R. Shafarevich Download Linear Algebra (Springer Undergraduate Texts in Mathematics)Linear Algebra (Springer Undergraduate Texts in Mathematics) Peter Petersen Download Lectures on Linear Partial Differential EquationsLectures on Linear Partial Differential Equations Gregory Eskin Download Introduction to Partial Differential Equations with MATLABIntroduction to Partial Differential Equations with MATLAB Jeffery Cooper Download Introduction to Nonlinear Dispersive Equations (Universitext)Introduction to Nonlinear Dispersive Equations (Universitext) Felipe Linares Download Hyperbolic Partial Differential Equations and Geometric Optics (Graduate Studies in Mathematics)Hyperbolic Partial Differential Equations and Geometric Optics (Graduate Studies in Mathematics) Jeffrey Rauch Download Elliptic Partial Differential Equations: Volume 2: Reaction-Diffusion Equations (Monographs in Mathematics)Elliptic Partial Differential Equations: Volume 2: Reaction-Diffusion Equations (Monographs in Mathematics) Vitaly Volpert Download Determinants and Their Applications in Mathematical Physics (Applied Mathematical Sciences)Determinants and Their Applications in Mathematical Physics (Applied Mathematical Sciences) Robert Vein Download Beginning Partial Differential Equations (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)Beginning Partial Differential Equations (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) Peter V. O'Neil Download An Introduction to the Mathematical Theory of Waves (Student Mathematical Library, V. 3)An Introduction to the Mathematical Theory of Waves (Student Mathematical Library, V. 3) Roger Knobel Download An Introduction to Lie Groups and the Geometry of Homogeneous Spaces (Student Mathematical Library, V. 22)An Introduction to Lie Groups and the Geometry of Homogeneous Spaces (Student Mathematical Library, V. 22) Andreas Arvanitogeorgos Download A Textbook on Ordinary Differential Equations, 2nd editionA Textbook on Ordinary Differential Equations, 2nd edition Shair Ahmad Download A textbook on Ordinary Differential EquationsA textbook on Ordinary Differential Equations Shair Ahmad Download A Dressing Method in Mathematical Physics (Mathematical Physics Studies)A Dressing Method in Mathematical Physics (Mathematical Physics Studies) Evgeny V. Doktorov Download A Basic Course in Partial Differential Equations (Graduate Studies in Mathematics)A Basic Course in Partial Differential Equations (Graduate Studies in Mathematics) Qing Han Download Mathematical Physics with Partial Differential EquationsMathematical Physics with Partial Differential Equations James Kirkwood