Share

The Painlevé Handbook

2008-11-23 Science
Download The Painlevé Handbook PDF Online Free

Author :
Release : 2008-11-23
Genre : Science
Kind : eBook
Book Rating : 919/5 ( reviews)

GET EBOOK


Book Synopsis The Painlevé Handbook by : Robert M. Conte

Download or read book The Painlevé Handbook written by Robert M. Conte. This book was released on 2008-11-23. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear differential or difference equations are encountered not only in mathematics, but also in many areas of physics (evolution equations, propagation of a signal in an optical fiber), chemistry (reaction-diffusion systems), and biology (competition of species). This book introduces the reader to methods allowing one to build explicit solutions to these equations. A prerequisite task is to investigate whether the chances of success are high or low, and this can be achieved without any a priori knowledge of the solutions, with a powerful algorithm presented in detail called the Painlevé test. If the equation under study passes the Painlevé test, the equation is presumed integrable. If on the contrary the test fails, the system is nonintegrable or even chaotic, but it may still be possible to find solutions. The examples chosen to illustrate these methods are mostly taken from physics. These include on the integrable side the nonlinear Schrödinger equation (continuous and discrete), the Korteweg-de Vries equation, the Hénon-Heiles Hamiltonians, on the nonintegrable side the complex Ginzburg-Landau equation (encountered in optical fibers, turbulence, etc), the Kuramoto-Sivashinsky equation (phase turbulence), the Kolmogorov-Petrovski-Piskunov equation (KPP, a reaction-diffusion model), the Lorenz model of atmospheric circulation and the Bianchi IX cosmological model. Written at a graduate level, the book contains tutorial text as well as detailed examples and the state of the art on some current research.

The Painlevé Handbook

2020-11-07 Science
Download The Painlevé Handbook PDF Online Free

Author :
Release : 2020-11-07
Genre : Science
Kind : eBook
Book Rating : 409/5 ( reviews)

GET EBOOK


Book Synopsis The Painlevé Handbook by : Robert Conte

Download or read book The Painlevé Handbook written by Robert Conte. This book was released on 2020-11-07. Available in PDF, EPUB and Kindle. Book excerpt: This book, now in its second edition, introduces the singularity analysis of differential and difference equations via the Painlevé test and shows how Painlevé analysis provides a powerful algorithmic approach to building explicit solutions to nonlinear ordinary and partial differential equations. It is illustrated with integrable equations such as the nonlinear Schrödinger equation, the Korteweg-de Vries equation, Hénon-Heiles type Hamiltonians, and numerous physically relevant examples such as the Kuramoto-Sivashinsky equation, the Kolmogorov-Petrovski-Piskunov equation, and mainly the cubic and quintic Ginzburg-Landau equations. Extensively revised, updated, and expanded, this new edition includes: recent insights from Nevanlinna theory and analysis on both the cubic and quintic Ginzburg-Landau equations; a close look at physical problems involving the sixth Painlevé function; and an overview of new results since the book’s original publication with special focus on finite difference equations. The book features tutorials, appendices, and comprehensive references, and will appeal to graduate students and researchers in both mathematics and the physical sciences.

Handbook of Nonlinear Partial Differential Equations, Second Edition

2016-04-19 Mathematics
Download Handbook of Nonlinear Partial Differential Equations, Second Edition PDF Online Free

Author :
Release : 2016-04-19
Genre : Mathematics
Kind : eBook
Book Rating : 24X/5 ( reviews)

GET EBOOK


Book Synopsis Handbook of Nonlinear Partial Differential Equations, Second Edition by : Andrei D. Polyanin

Download or read book Handbook of Nonlinear Partial Differential Equations, Second Edition written by Andrei D. Polyanin. This book was released on 2016-04-19. Available in PDF, EPUB and Kindle. Book excerpt: New to the Second Edition More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some exact methods and transformations Symbolic and numerical methods for solving nonlinear PDEs with MapleTM, Mathematica®, and MATLAB® Many new illustrative examples and tables A large list of references consisting of over 1,300 sources To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology. They outline the methods in a schematic, simplified manner and arrange the material in increasing order of complexity.

Orthogonal Polynomials and Painlevé Equations

2018 Mathematics
Download Orthogonal Polynomials and Painlevé Equations PDF Online Free

Author :
Release : 2018
Genre : Mathematics
Kind : eBook
Book Rating : 947/5 ( reviews)

GET EBOOK


Book Synopsis Orthogonal Polynomials and Painlevé Equations by : Walter Van Assche

Download or read book Orthogonal Polynomials and Painlevé Equations written by Walter Van Assche. This book was released on 2018. Available in PDF, EPUB and Kindle. Book excerpt: There are a number of intriguing connections between Painlev equations and orthogonal polynomials, and this book is one of the first to provide an introduction to these. Researchers in integrable systems and non-linear equations will find the many explicit examples where Painlev equations appear in mathematical analysis very useful. Those interested in the asymptotic behavior of orthogonal polynomials will also find the description of Painlev transcendants and their use for local analysis near certain critical points helpful to their work. Rational solutions and special function solutions of Painlev equations are worked out in detail, with a survey of recent results and an outline of their close relationship with orthogonal polynomials. Exercises throughout the book help the reader to get to grips with the material. The author is a leading authority on orthogonal polynomials, giving this work a unique perspective on Painlev equations.

Divergent Series, Summability and Resurgence III

2016-06-28 Mathematics
Download Divergent Series, Summability and Resurgence III PDF Online Free

Author :
Release : 2016-06-28
Genre : Mathematics
Kind : eBook
Book Rating : 002/5 ( reviews)

GET EBOOK


Book Synopsis Divergent Series, Summability and Resurgence III by : Eric Delabaere

Download or read book Divergent Series, Summability and Resurgence III written by Eric Delabaere. This book was released on 2016-06-28. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this volume is two-fold. First, to show how the resurgent methods introduced in volume 1 can be applied efficiently in a non-linear setting; to this end further properties of the resurgence theory must be developed. Second, to analyze the fundamental example of the First Painlevé equation. The resurgent analysis of singularities is pushed all the way up to the so-called “bridge equation”, which concentrates all information about the non-linear Stokes phenomenon at infinity of the First Painlevé equation. The third in a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists who are interested in divergent power series and related problems, such as the Stokes phenomenon. The prerequisites are a working knowledge of complex analysis at the first-year graduate level and of the theory of resurgence, as presented in volume 1.

You may also like...