This book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in particular, about the current state-of-the art and new results in: Nonlinear water waves: resonance, solitons, focusing, Bose-Einstein condensation, as well as and their relevance for the sea environment (sea-wind interaction, sand bed forms, fiber clustering) Pattern formation in non-equilibrium media: soap films, chimera patterns in oscillating media, viscoelastic Couette-Taylor flow, flow in the wake behind a heated cylinder, other pattern formation. The editors and authors dedicate this book to the memory of Alexander Ezersky, Professor of Fluid Mechanics at the University of Caen Normandie (France) from September 2007 to July 2016. Before 2007, he had served as a Senior Scientist at the Institute of Applied Physics of the Russian Academy of Sciences in Nizhny Novgorod (Russia). The chapters have been written by leading scientists in Nonlinear Physics, and the topics chosen so as to cover all the fields to which Prof. Ezersky himself contributed, by means of experimental, theoretical and numerical approaches. The volume will appeal to advanced students and researchers studying nonlinear waves and pattern dynamics, as well as other scientists interested in their applications in various natural media.

On March 15, 1901, Henri B' enard defended his thesis entitled "Les Tourbillons cellulaires dans une nappe liquide propageant de la chaleur par convection en 1 r' egime permanent" at the University of Paris, Sorbonne. The results contained in this thesis have been at the origin of recent intensive research activities on c- lular structures observed in many physicochemical systems far from equilibrium: instabilities, spatio-temporal patterns, chaos, and turbulence. The French Physical Society organized a scienti?c meeting to commemorate the centenary of B' enard's thesis, at the Ecole Sup' erieure de Physique et Chimie Industrielles de Paris (ESPCI). This meeting, which gathered approximately one hundred scientists and graduate students working in nonlinear science, was honored by the presence of the director of the ESPCI, Professor Pierre-Gilles de Gennes, Nobel laureate in physics (1991), who gave the opening talk. At the conference, lectures were given by internationally recognized scholars who have contributed to the development of B' enard's work: J.E. Wesfreid, P. Manneville,Y.Pomeau,M.Velarde,J.Gollub,M.Provansal,G.Nicolis,B.C- taing,andP.Coullet.Apostersessionandaroundtableonfurtherdevelopments in nonlinear physics were organized. In the present book, we have extended the list of contributors in order to cover all the aspects involved with B' enard's work, with a main focus on th- mal convection, on B' enard-Marangoni instability and on B' enard-von Karman instability. WewouldliketothankDr.HansKoelschfromSpringerforthepublicationof this monography in the Springer Tracts in Modern Physics series. We ackno- edge a critical reading by C.D. Mitescu and a very helpful technical assistance from Olivier Crumeyrolle.

On March 15, 1901, Henri B enard defended his thesis entitled "Les Tourbillons cellulaires dans une nappe liquide propageant de la chaleur par convection en 1 r egime permanent" at the University of Paris, Sorbonne. The results contained in this thesis have been at the origin of recent intensive research activities on c- lular structures observed in many physicochemical systems far from equilibrium: instabilities, spatio-temporal patterns, chaos, and turbulence. The French Physical Society organized a scienti?c meeting to commemorate the centenary of B enard's thesis, at the Ecole Sup erieure de Physique et Chimie Industrielles de Paris (ESPCI). This meeting, which gathered approximately one hundred scientists and graduate students working in nonlinear science, was honored by the presence of the director of the ESPCI, Professor Pierre-Gilles de Gennes, Nobel laureate in physics (1991), who gave the opening talk. At the conference, lectures were given by internationally recognized scholars who have contributed to the development of B enard's work: J.E. Wesfreid, P. Manneville, Y.Pomeau, M.Velarde, J.Gollub, M.Provansal, G.Nicolis, B.C- taing, andP.Coullet.Apostersessionandaroundtableonfurtherdevelopments in nonlinear physics were organized. In the present book, we have extended the list of contributors in order to cover all the aspects involved with B enard's work, with a main focus on th- mal convection, on B enard-Marangoni instability and on B enard-von Karman instability. WewouldliketothankDr.HansKoelschfromSpringerforthepublicationof this monography in the Springer Tracts in Modern Physics series. We ackno- edge a critical reading by C.D. Mitescu and a very helpful technical assistance from Olivier Crumeyrolle."