Description
Book SynopsisReveals 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 ReviewThis 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
