Aspects of Integrability of Differential Systems and Fields : A Mathematical Primer for Physicists / by Costas J. Papachristou.

Format:

Book

Author/Creator:

Papachristou, Costas J., author.

Contributor:

SpringerLink (Online service)

Series:

Physics and Astronomy (Springer-11651)

SpringerBriefs in physics 2191-5423

SpringerBriefs in Physics, 2191-5423

Language:

English

Subjects (All):

Physics.

Mathematical physics.

Differential equations.

Differential equations, Partial.

Mathematical Methods in Physics.

Mathematical Physics.

Ordinary Differential Equations.

Partial Differential Equations.

Local Subjects:

Mathematical Methods in Physics.

Mathematical Physics.

Ordinary Differential Equations.

Partial Differential Equations.

Physical Description:

1 online resource (VIII, 94 pages) : 20 illustrations.

Edition:

First edition 2019.

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2019.

System Details:

text file PDF

Summary:

This book serves as an introduction to the concept of integrability as it applies to systems of differential equations as well as to vector-valued fields. The author focuses on specific aspects of integrability that are often encountered in a variety of problems in applied mathematics, physics and engineering. The following general cases of integrability are examined: (a) path-independence of line integrals of vector fields on the plane and in space; (b) integration of a system of ordinary differential equations by using first integrals; and (c) integrable systems of partial differential equations. Special topics include the integration of analytic functions and some elements from the geometric theory of differential systems. Certain more advanced subjects, such as Lax pairs and Bäcklund transformations, are also discussed. The book is written at an intermediate level for educational purposes. The presentation is as simple as the topics allow, often sacrificing mathematical rigor in favor of pedagogical efficiency.

Contents:

Integrability on the plane and in space

Integrability on the complex plane

Ordinary differential equations

Systems of ordinary differential equations

Differential systems: Geometric viewpoint

Integrable systems of partial differential equations.

Other Format:

Printed edition:

ISBN:

978-3-030-35002-4

9783030350024

Access Restriction:

Restricted for use by site license.