Description

Book Synopsis
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.

Trade Review
This book challenges and intrigues from beginning to end. It would be a treat to use for a capstone course or senior seminar." —William J. Satzer, MAA Reviews on Glimpses of Soliton Theory (First Edition)

Table of Contents
  • Differential equations
  • Developing PDE intuition
  • The story of solitons
  • Elliptic curves and KdV traveling waves
  • KdV $n$-solitons and $\tau$-functions
  • Multiplying and factoring differential operators
  • Eigenfunctions and isospectrality
  • Lax form for KdV and other soliton equations
  • The KP equation and bilinear KP equation
  • $\Gamma_{2,4}$ and the bilinear KP equation
  • Pseudo-differential operators and the KP hierarchy
  • $\Gamma{k,n}$ and the bilinear KP hierarchy
  • Concluding remarks
  • Mathematica guide
  • Complex numbers
  • Ideas for independent projects
  • References
  • Glossary of symbols
  • Index

Glimpses of Soliton Theory The Algebra and

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    A Paperback by Alex Kasman

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      Book details

      Publisher American Mathematical Society
      Published 6/30/2023 12:00:00 AM
      ISBN-13 9781470472627
      978-1470472627
      ISBN-10 1470472627
      Also in:
      Mathematics Algebra Not Just Books Stationery

      Description

      Book Synopsis
      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.

      Trade Review
      This book challenges and intrigues from beginning to end. It would be a treat to use for a capstone course or senior seminar." —William J. Satzer, MAA Reviews on Glimpses of Soliton Theory (First Edition)

      Table of Contents
      • Differential equations
      • Developing PDE intuition
      • The story of solitons
      • Elliptic curves and KdV traveling waves
      • KdV $n$-solitons and $\tau$-functions
      • Multiplying and factoring differential operators
      • Eigenfunctions and isospectrality
      • Lax form for KdV and other soliton equations
      • The KP equation and bilinear KP equation
      • $\Gamma_{2,4}$ and the bilinear KP equation
      • Pseudo-differential operators and the KP hierarchy
      • $\Gamma{k,n}$ and the bilinear KP hierarchy
      • Concluding remarks
      • Mathematica guide
      • Complex numbers
      • Ideas for independent projects
      • References
      • Glossary of symbols
      • Index

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