Recent Developments in Integrable Systems and Related Topics of Mathematical Physics : Kezenoi Am Russia 2016 Victor Buchstaber Sotiris Konstantinou Rizos and Alexander Mikhailov Introduction P. G. Grinevich and P. M. Santini Numerical instability of the Akhmediev breather and a finite gap model of it V.Yu. Novokshenov Movable poles of Painlevé I transcendents and singularities of monodromy data manifolds Vladimir Sokolov Elliptic Calogero Moser Hamiltonians and compatible Poisson brackets A.V. Tsiganov Bäcklund transformations and new integrable systems on the plane V. Rubtsov Quadro cubic Cremona transformations and Feigin Odesskii Sklyanin algebras with 5 generators Dimitri Gurevich and Pavel Saponov From Reflection Equation Algebra to Braided Yangians G. Sharygin and A. Konyaev Survey of the Deformation Quantization of Commutative Families Dmitry Millionshchikov Graded Thread Modules over the Positive Part of the Witt (Virasoro) Algebra Andrei Shafarevich Localized solutions of the Schrödinger equation on hybrid spaces. Relation to the behavior of geodesics and to analytic number theory A. V. Fursikov Normal equation generated from Helmholtz system: nonlocal stabilization by starting control and properties of stabilized solutions This volume whose contributors include leading researchers in their field covers a wide range of topics surrounding Integrable Systems from theoretical developments to applications. Comprising a unique collection of research articles and surveys the book aims to serve as a bridge between the various areas of Mathematics related to Integrable Systems and Mathematical Physics. Recommended for postgraduate students and early career researchers who aim to acquire knowledge in this area in preparation for further research this book is also suitable for established researchers aiming to get up to speed with recent developments in the area and may very well be used as a guide for further study