Nonlinear Systems and Their Remarkable Mathematical Structures

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.

Part A: Integrability, Lax Pairs and Symmetry. A1. Reciprocal transformations and their role in the integrability and classification of PDEs. A2. Contact Lax pairs and associated (3+1)-dimensional integrable dispersionless systems. A3. Lax Pairs for Edge-constrained Boussinesq Systems of Partial Difference Equations. A4. Lie point symmetries of delay ordinary differential equations. A5. The symmetry approach to integrability: recent advances. A6. Evolution of the concept of λ--symmetry and main applications. A7. Heir-equations for partial dfferential equations: a 25-year review. Part B: Algebraic and Geometric Methods. B1. Coupled nonlinear Schrodinger equations: spectra and instabilities of plane waves. B2. Rational solutions of Painleve systems. B3. Cluster algebras and discrete integrability. B4. A review of elliptic difference Painleve equations. B5. Linkage mechanisms governed by integrable deformations of discrete space curves. B6. The Cauchy problem of the Kadomtsev-Petviashvili hierarchy and infinite-dimensional groups. B7. Wronskian solutions of integrable systems. Part C: Applications. C1. Global gradient catastrophe in a shallow water model: evolution unfolding by stretched coordiates. C2. Vibrations of an elastic bar, isospectral deformations, and modified Camassa-Holm equations. C3. Exactly solvable (discrete) quantum mechanics and new orthogonal polynomials.