Nonlinear systems and their remarkable mathematical structures. Volumes 1, 2, 3

**__Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 1__** aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Written by experts, each chapter is self-contained and aims to clearly illustrate some of the mathematical theories of nonlinear systems. The book should be suitable for some graduate and postgraduate students in mathematics, the natural sciences, and engineering sciences, as well as for researchers (both pure and applied) interested in nonlinear systems. The common theme throughout the book is on solvable and integrable nonlinear systems of equations and methods/theories that can be applied to analyze those systems. Some applications are also discussed. **Features:** * Collects contributions on recent advances in the subject of nonlinear systems * Aims to make the advanced mathematical methods accessible to the non-expert in this field * Written to be accessible to some graduate and postgraduate students in mathematics and applied mathematics * Serves as a literature source in nonlinear systems Content: Part A: Nonlinear Integrable SystemsA1. Systems of nonlinearly-coupled differential equations solvableF CalogeroA2. Integrable nonlinear PDEs on the half-lineA S Fokas and B PelloniA3. Detecting discrete integrability: the singularity approachGrammaticos, A Ramani, R Willox and T MaseA4. Elementary introduction to discrete soliton equations J HietarintaA5. New results on integrability of the Kahan-Hirota-Kimura discretizationsYu B Suris and M PetreraPart B: Solution Methods and Solution StructuresB1. Dynamical systems satisfied by special polynomials and related isospectral matrices defined in terms of their zeros O BihunB2. Singularity methods for meromorphic solutions of differential equationsR Conte, T W Ng and C WuB3. Pfeiffer-Sato solutions of Buhl's problem and a Lagrange-D'Alembert principle for Heavenly equations O E Hentosh, Ya A Prykarpatsky, D Blackmore and A PrykarpatskiB4. Superposition formulae for nonlinear integrable equations in bilinear form X B HuB5. Matrix solutions for equations of the AKNS system C SchieboldB6. Algebraic traveling waves for the generalized KdV-Burgers equation and the Kuramoto-Sivashinsky equationC VallsPart C: Symmetry Methods for Nonlinear SystemsC1. Nonlocal invariance of the multipotentialisations of the Kupershmidt equation and its higher-order hierarchies M Euler and N EulerC2. Geometry of normal forms for dynamical systems G GaetaC3. Computing symmetries and recursion operators of evolutionary super-systems using the SsTools environment A V Kiselev, A O Krutov and T WolfC4. Symmetries of It^o stochastic differential equations and their applications R KozlovC5. Statistical symmetries of turbulenceM Oberlack, M Wac lawczyk and V GrebenevPart D: Nonlinear Systems in ApplicationsD1. Integral transforms and ordinary differential equations of infinite order A Chavez, H Prado and E G ReyesD2. The role of nonlinearity in geostrophic ocean flows on a sphere A Constantin and R S JohnsonD3. Review of results on a system of type many predators - one prey A V Osipov and G S oderbackaD4. Ermakov-type systems in nonlinear physics and continuum mechanicsC Rogers and W K Schief "The book aims to describe some recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete)"-- Nonlinear Systems and Their Remarkable Mathematical Structures aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Written by experts, each chapter is self-contained and aims to clearly illustrate some of the mathematical theories of nonlinear systems. The book should be suitable for some graduate and postgraduate students in mathematics, the natural sciences, and engineering sciences, as well as for researchers (both pure and applied) interested in nonlinear systems. The common theme throughout the book is on solvable and integrable nonlinear systems of equations and methods/theories that can be applied to analyze those systems. Some applications are also discussed. Features Collects contributions on recent advances in the subject of nonlinear systems Aims to make the advanced mathematical methods accessible to the non-expert in this field Written to be accessible to some graduate and postgraduate students in mathematics and applied mathematics Serves as a literature source in nonlinear systems 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. 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.