Nonlinear Systems and Their Remarkable Mathematical Structures

The third volume consists of a collection of contributions by world-leading experts in the subject of nonlinear DE and nonlinear dynamical systems (both continuous and discrete), but in this instance only featuring contributions by leading Chinese scientists who also work in China.

The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just like the first two volumes, consists of contributions by world-leading experts in the subject of nonlinear systems, but in this instance only featuring contributions by leading Chinese scientists who also work in China (in some cases in collaboration with western scientists). Features

• Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area .

• Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering Sciences.

• Written in a careful pedagogical manner by those experts who have been involved in the research themselves, and each contribution is reasonably self-contained.

  Autorentext

  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

Klappentext

The third volume consists of a collection of contributions by world-leading experts in the subject of nonlinear DE and nonlinear dynamical systems (both continuous and discrete), but in this instance only featuring contributions by leading Chinese scientists who also work in China.

Inhalt

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 -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.