We briefly review new trends in how the notion of complete integrability of dynamical systems and their quantum counterpart developed over the last four decades. We describe a new technique for working with integrable models and outline its main applications.

PACS: 02.30.Ik, 45.20.Jj, 75.10.Pq (all) DOI: 10.3367/UFNe.0183.201305b.0487 URL: https://ufn.ru/en/articles/2013/5/b/ 000322890700002 2-s2.0-84882953609 2013PhyU...56..465F Citation: Faddeev L D "New life of complete integrability" Phys. Usp. 56 465–472 (2013) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 21st, February 2013, accepted: 27th, February 2013 Оригинал: Фаддеев Л Д «Новая жизнь полной интегрируемости» УФН 183 487–495 (2013); DOI: 10.3367/UFNr.0183.201305b.0487