The symmetry approach to integrability: recent advances
Abstract
We provide a concise introduction to the symmetry approach to integrability. Some results on integrable evolution and systems of evolution equations are reviewed. Quasi-local recursion and Hamiltonian operators are discussed. We further describe non-abelian integrable equations, especially matrix (ODE and PDE) systems. Some non-evolutionary integrable equations are studied using a formulation of formal recursion operators that allows to study non-diagonalisable systems of evolution equations.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2019
- DOI:
- 10.48550/arXiv.1904.01953
- arXiv:
- arXiv:1904.01953
- Bibcode:
- 2019arXiv190401953H
- Keywords:
-
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- To be published in: Nonlinear Systems and Their Remarkable Mathematical Structures, Vol. 2, N. Euler and M.C. Nucci (editors), CRC Press, Boca Raton, 2019. arXiv admin note: text overlap with arXiv:1711.10624