This book illustrates the powerful interplay between topological, algebraic and complex analytical methods, within the field of integrable systems, by addressing several theoretical and practical aspects. Contemporary integrability results, discovered in the last few decades, are used within different areas of mathematics and physics.
Integrable Systems incorporates numerous concrete examples and exercises, and covers a wealth of essential material, using a concise yet instructive approach. This book is intended for a broad audience, ranging from mathematicians and physicists to students pursuing graduate, Masters or further degrees in mathematics and mathematical physics. It also serves as an excellent guide to more advanced and detailed reading in this fundamental area of both classical and contemporary mathematics.
1. Symplectic Manifolds.
2. Hamilton–Jacobi Theory.
3. Integrable Systems.
4. Spectral Methods for Solving Integrable Systems.
5. The Spectrum of Jacobi Matrices and Algebraic Curves.
6. Griffiths Linearization Flows on Jacobians.
7. Algebraically Integrable Systems.
8. Generalized Algebraic Completely Integrable Systems.
9. The Korteweg–de Vries Equation.
10. KP–KdV Hierarchy and Pseudo-differential Operators.
Ahmed Lesfari is a professor of mathematics at Chouaib Doukkali University, Morocco. He studied mathematics at the University of Louvain (U.C.L.), Belgium, where he obtained his Doctor of Science degree. His mathematical interests are in integrable systems and geometry.
Table of Contents
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