Nonlinear Systems and Their Remarkable Mathematical Structures

Norbert Euler is currently a visiting professor at the International Center of Sciences A.C. (Cuernavaca, Mexico). He has been teaching a wide variety of mathematics courses at both the undergraduate and postgraduate level at several universities worldwide for more than 25 years. He is an active researcher and has to date published over 80 peer reviewed research articles in the subject of nonlinear systems and is a co-author of several books. He is also involved in editorial work for some international journals.Da-jun Zhang is currently a full professor at Shanghai University in China. His research focuses on integrability of discrete and continuous nonlinear systems, and particularly, discrete integrable systems. He has published over 120 peer reviewed research articles in the subject of integrable systems. He has served as scientific committee member for some international conferences. He is also involved in editorial work for some international journals

"The book surveys recent progress in nonlinear differential equations and nonlinear dynamical systems. With contributions written by internationally well-known experts, some modern aspects of nonlinear science are discussed in detail, especially those related to integrable systems."– Adrian Constantin, University of Vienna"This book covers the most active research domains on integrability not only in China, but also abroad.At the invitation of the two editors, all the authors, experts in their field, made a real effort to make the state-of-the-art accessible to graduate students and young researchers."– Robert Conte, Associate Research Director, Université Paris-Saclay"The third volume of Nonlinear Systems and Their Remarkable Mathematical Structures is an outstanding contribution to a large area of mathematics mathematical physics.Quite remarkably, the book contains very recent and sophisticated advances, but, at the same time, it remains accessible to a wide audience. It can be recommended to graduate students and young researchers willing to familiarize themselves with the subject. The book contains introductory articles written by leading experts, and this make it possible for the reader to cover a greater distance in a short time, to arrive at the front line of contemporary research."– Valentin Ovsienko, CNRS, University of Reims Champagne Ardenne

• Part A: Integrability and Symmetries. A1. The BKP hierarchy and the modified BKP hierarchy. A2. Elementary introduction to the direct linearisation of integrable systems. A3. Discrete Boussinesq-type equations. A4. The study of integrable hierarchies in terms of Liouville correspondences. A5. Darboux transformations for supersymmetric integrable systems: A brief review. A6. Nonlocal symmetries of nonlinear integrable systems. A7. High-order soliton matrix for an extended nonlinear Schrödinger equation. A8. Darboux transformation for integrable systems with symmetries. A9. Frobenius manifolds and Orbit spaces of reflection groups and their extensions. Part B: Algebraic, Analytic and Geometric Methods. B1. On finite Toda type lattices and multipeakons of the Camassa-Holm type equations. B2. Long-time asymptotics for the generalized coupled derivative nonlinear Schrödinger equation. B3. Bilinearization of nonlinear integrable evolution equations: Recursion operator approach. B4. Rogue wave patterns and modulational instability in nonlinear Schrödinger hierarchy. B5. Algebro-geometric solutions to the modified Blaszak-Marciniak lattice hierarchy. B6. Long-time asymptotic behavior of the modified Schrödinger equation via θ-steepest descent method. B7. Two hierarchies of multiple solitons and soliton molecules of (2+1)-dimensional Sawada-Kotera type equation. B8. Dressing the boundary: exact solutions of soliton equations on the half-line. B9. From integrable spatial discrete hierarchy to integrable nonlinear PDE hierarchy.