- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
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
Contents
Part A: Nonlinear Integrable Systems A1. Systems of nonlinearly-coupled differential equations solvable A2. Integrable nonlinear PDEs on the half-line A3. Detecting discrete integrability: the singularity approach A4. Elementary introduction to discrete soliton equations A5. New results on integrability of the Kahan-Hirota-Kimura discretizations Part B: Solution Methods and Solution Structures B1. Dynamical systems satisfied by special polynomials and related isospectral matrices defined in terms of their zeros B2. Singularity methods for meromorphic solutions of differential equations B3. Pfeiffer-Sato solutions of Buhl's problem and a Lagrange-D'Alembert principle for Heavenly equations B4. Superposition formulae for nonlinear integrable equations in bilinear form B5. Matrix solutions for equations of the AKNS system B6. Algebraic traveling waves for the generalized KdV-Burgers equation and the Kuramoto-Sivashinsky equation Part C: Symmetry Methods for Nonlinear Systems C1. Nonlocal invariance of the multipotentialisations of the Kupershmidt equation and its higher-order hierarchies C2. Geometry of normal forms for dynamical systems C3. Computing symmetries and recursion operators of evolutionary super-systems using the SsTools environment C4. Symmetries of It^o stochastic differential equations and their applications C5. Statistical symmetries of turbulence Part D: Nonlinear Systems in Applications D1. Integral transforms and ordinary differential equations of infinite order D2. The role of nonlinearity in geostrophic ocean flows on a sphere D3. Review of results on a system of type many predators - one prey D4. Ermakov-type systems in nonlinear physics and continuum mechanics
