Nonlinear Systems and Their Remarkable Mathematical Structures

Volume 1

Norbert Euler (Redaktør)

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. Les mer
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Paperback
Legg i
Vår pris: 725,-

(Paperback) Fri frakt!
Leveringstid: Sendes innen 21 dager
På grunn av Brexit-tilpasninger og tiltak for å begrense covid-19 kan det dessverre oppstå forsinket levering.

Om boka

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

Fakta

Innholdsfortegnelse

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



Om forfatteren

Norbert Euler is a professor of mathematics at Lulea University of Technology in Sweden. He is teaching a wide variety of mathematics courses at both the undergraduate and postgraduate level and has done so at several universities worldwide for more than 25 years. He is an active researcher and has to date published over 70 peer reviewed research articles in the subject of nonlinear systems and he is a co-author of several books. He is also involved in editorial work for some international journals, and he is the Editor-in-Chief of the Journal of Nonlinear Mathematical Physics since 1997.