TL;DR
This paper provides an introductory overview of integrable systems, covering key concepts like the Arnold-Liouville theorem, inverse scattering, Hamiltonian methods, and Lie symmetries, suitable for advanced undergraduates.
Contribution
It offers a foundational lecture-based exposition of integrable systems, making complex topics accessible to students with basic calculus and ODE knowledge.
Findings
Introduces the Arnold-Liouville theorem and inverse scattering transform.
Explains Hamiltonian methods in soliton theory.
Discusses Lie point symmetries in integrable systems.
Abstract
These notes are based on lecture courses I gave to third year mathematics students at Cambridge. They could form a basis of an elementary one--term lecture course on integrable systems covering the Arnold-Liouville theorem, inverse scattering transform, Hamiltonian methods in soliton theory and Lie point symmetries. No knowledge beyond basic calculus and ordinary differential equation is assumed.
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Taxonomy
TopicsNonlinear Waves and Solitons · Numerical methods for differential equations · Quantum chaos and dynamical systems