Nonlinear Systems and Their Remarkable Mathematical Structures Volume 2

Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 2 is written in a careful pedagogical manner by experts from the field of nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). This book aims to clearly illustrate the mathematical theories of nonlinear systems and its progress to both non-experts and active researchers in this area. Just like the first volume, this book is suitable for graduate students in mathematics, applied mathematics and engineering sciences, as well as for researchers in the subject of differential equations and dynamical systems. Features Collects contributions on recent advances in the subject of nonlinear systems Aims to make the advanced mathematical methods accessible to the non-experts Suitable for a broad readership including researchers and graduate students in mathematics and applied mathematics

Part A: Integrability, Lax Pairs and Symmetry Chapter A1: Reciprocal transformations and their role in the integrability and classification of PDEs P Albares, P G Estevez, and C Sardon Chapter A2: Contact Lax pairs and associated (3+1)-dimensional integrable dispersionless systems M Blaszak and A Sergyeyev Chapter A3: Lax Pairs for edge-constrained Boussinesq Systems of partial difference equations T J Bridgman and W Hereman Chapter A4: Lie point symmetries of delay ordinary differential equations V A Dorodnitsyn, R Kozlov, S V Meleshko, and P Winternitz Chapter A5: The symmetry approach to integrability: recent advances R Hernandez Heredero and V Sokolov Chapter A6: Evolution of the concept of ?-symmetry and main Applications C Muriel and J L Romero Chapter A7: Heir-equations for partial differential equations:a 25-year review M C Nucci Part B: Algebraic and Geometric Methods Chapter B1: Coupled nonlinear Schrödinger equations: spectra and instabilities of plane waves A Degasperis, S Lombardo, and M Sommacal Chapter B2: Rational solutions of Painlevé systems D Gomez-Ullate, Y Grandati, and R Milson Chapter B3: Cluster algebras and discrete integrability A N W Hone, P Lampe, and T E Kouloukas Chapter B4: A review of elliptic difference Painlevé equations N Joshi and N Nakazono Chapter B5: Linkage mechanisms governed by integrable deformations of discrete space curves S Kaji, K Kajiwara, and H Park Chapter B6: The Cauchy problem of the Kadomtsev-Petviashvili hierarchy and infinite-dimensional groups J-P Magnot and E G Reyes Chapter B7: Wronskian solutions of integrable systems D-j Zhang Part C: Applications Chapter C1: Global gradient catastrophe in a shallow water model: evolution unfolding by stretched coordinates R Camassa Chapter C2: Vibrations of an elastic bar, isospectral deformations, and modified Camassa-Holm equations X Chang and J Szmigielski Chapter C3: Exactly solvable (discrete) quantum mechanics and new orthogonal polynomials R Sasaki

Norbert Euler is professor of mathematics at Jinan University in Guangzhou, P. R. China, and visiting research professor at the Centro Internacional de Ciencias AC in Cuernavaca, Mexico. Until April 2019 he was professor of mathematics at Luleå University of Technology in Sweden, where he was teaching and researching for 23 years. His main research interests are in the subject of nonlinear mathematical physics, in particular nonlinear ordinary and partial differential equations and integrable systems, and he has published approximately 80 peer reviewed research articles and co-authored several books. He is involved in editorial work for journals, and has been the editor-in-chief of the Journal of Nonlinear Mathematical Physics since 1997. Maria Clara Nucci is associate professor of mathematical physics at University of Perugia, where she graduated in mathematics summa cum laude. Between 1986 and 1991 she was a visiting assistant professor at Georgia Institute of Technology, Atlanta, US. She has also been invited by universities in Australia, Canada, France, Germany, Greece, Sweden, UK, and the US. She has presented her research at many international congresses and workshops. From 1995–2009 she was associate editor of Journal of Mathematical Analysis and Applications, and since 2005 has been a member of the editorial board of Journal of Nonlinear Mathematical Physics. She is author or co-author of more than 100 publications, and has wide ranging research interests, from fluid to rigid body mechanics, epidemiology to astrophysics, and history of mathematics to quantum mechanics.