Integrable Systems
Lax pairs, inverse scattering, and quantum integrability.
Integrable Systems. Lax pairs, inverse scattering, and quantum integrability.
Foundations and canonical references
The standard treatments of integrable systems approach the subject from complementary angles. Vanhaecke, Integrable Systems in the Realm of Algebraic Geometry (2001) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Faddeev, Hamiltonian Methods in the Theory of Solitons (2007) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for integrable systems include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2001Integrable Systems in the Realm of Algebraic Geometryvanhaecke-2001
- textbook · primary · 2007Hamiltonian Methods in the Theory of Solitonsfaddeev-2007, takhtajan-2007
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