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Integrable Systems

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Author(s): A. Ashton, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part II Lecture Notes
Publisher: University of Cambridge
Year: 2016

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; integration; integrable

Introduction
Integrability of ODE's
Vector fields and flow maps
Hamiltonian dynamics
Canonical transformations
The Arnold-Liouville theorem
Partial Differential Equations
KdV equation
Sine–Gordon equation
Backlund transformations
Inverse scattering transform
Forward scattering problem
Continuous spectrum
Discrete spacetime and bound states
Summary of forward scattering problem
Inverse scattering problem
Lax pairs
Evolution of scattering data
Continuous spectrum (lambda = k2 > 0)
Discrete spectrum (lambda = -kappa2 < 0)
Summary of inverse scattering transform
Reflectionless potentials
Infinitely many first integrals
Structure of integrable PDEs
Infinite dimensional Hamiltonian system
Bihamiltonian systems
Zero curvature representation
From Lax pairs to zero curvature
Symmetry methods in PDEs
Lie groups and Lie algebras
Vector fields and one-parameter groups of transformations
Symmetries of differential equations
Jets and prolongations
Painleve test and integrability
Index