English

The symmetry approach to integrability: recent advances

Exactly Solvable and Integrable Systems 2019-04-04 v1

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.

Keywords

Cite

@article{arxiv.1904.01953,
  title  = {The symmetry approach to integrability: recent advances},
  author = {Rafael Hernández Heredero and Vladimir Sokolov},
  journal= {arXiv preprint arXiv:1904.01953},
  year   = {2019}
}

Comments

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