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Nonlinear Systems and Their Remarkable Mathematical Structures : Volume I.

Author: Norbert Euler
Publisher: Milton : Chapman and Hall/CRC, 2018.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:

"The book aims to describe some recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete)"--

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Genre/Form: Electronic books
Additional Physical Format: Print version:
Euler, Norbert.
Nonlinear Systems and Their Remarkable Mathematical Structures : Volume I.
Milton : Chapman and Hall/CRC, ©2018
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Norbert Euler
ISBN: 9780429893810 0429893817 9780429893803 0429893809 9780429893797 0429893795 9780429470462 0429470460
OCLC Number: 1076803687
Notes: 3. Heavenly equations: Lie-algebraic integrability scheme
Description: 1 online resource (599 pages)
Contents: Cover; Half Title; Title; Copyrights; Contents; Preface; The Authors; Part A; A1. Systems of nonlinearly-coupled di erential equations solvable by algebraic operations F Calogero; 1. Introduction; 2. The main idea and some key identities; 3. Two examples of systems of nonlinearly-coupled ODEs solvable by algebraic operations; 4. A di erential algorithm to evaluate all the zeros of a generic polynomial of arbitrary degree; 5. Extensions; A2. Integrable nonlinear PDEs on the half-line A S Fokas and B Pelloni; 1. Introduction; 2. Transforms and Riemann-Hilbert problems 3. The structure of integrable PDEs: Lax pair formulation4. An integral transform for nonlinear boundary value problems; 5. Further considerations; A3. Detecting discrete integrability: the singularity approach B Grammaticos, A Ramani, R Willox and T Mase; 1. Introduction; 2. Singularity con nement; 3. The full-deautonomisation approach; 4. Halburd's exact calculation of the degree growth; 5. Singularities and spaces of initial conditions; A4. Elementary introduction to discrete soliton equations J Hietarinta; 1. Introduction; 2. Basic set-up for lattice equations 3. Symmetries and hierarchies4. Lax pairs; 5. Continuum limits; 6. Discretizing a continuous equation; 7. Integrability test; 8. Summary; A5. New results on integrability of the Kahan-Hirota-Kimura discretizations Yu B Suris and M Petrera; 1. Introduction; 2. General properties of the Kahan-Hirota-Kimura discretization; 3. Novel observations and results; 4. The general Clebsch ow; 5. The rst Clebsch ow; 6. The Kirchho case; 7. Lagrange top; 8. Concluding remarks; Part B B1. Dynamical systems satisfied by special polynomials and related isospectral matrices de ned in terms of their zeros O Bihun1. Introduction; 2. Zeros of generalized hypergeometric polynomial with two parameters and zeros of Jacobi polynomials; 3. Zeros of generalized hypergeometric polynomials; 4. Zeros of generalized basic hypergeometric polynomials; 5. Zeros of Wilson and Racah polynomials; 6. Zeros of Askey-Wilson and q-Racah polynomials; 7. Discussion and Outlook; B2. Singularity methods for meromorphic solutions of differential equations R Conte, T W Ng and C F Wu; 1. Introduction 2. A simple pedagogical example3. Lessons from this pedagogical example; 4. Another characterization of elliptic solutions: the subequation method; 5. An alternative to the Hermite decomposition; 6. The important case of amplitude equations; 7. Nondegenerate elliptic solutions; 8. Degenerate elliptic solutions; 9. Current challenges and open problems; B3. Pfei er-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 Prykarpatski; 1. Introduction; 2. Lax{Sato compatible systems of vector eld equations

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The theory of integrable systems studies remarkable equations of mathematical physics which are, in a sense, exactly solvable and possess regular behaviour. Such equations play a fundamental role in Read more...

 
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