Last edited by Mikazilkree

Monday, July 20, 2020 | History

7 edition of **Symmetries and differential equations** found in the catalog.

- 389 Want to read
- 5 Currently reading

Published
**1989**
by Springer-Verlag in New York
.

Written in English

- Differential equations -- Numerical solutions.,
- Differential equations, Partial -- Numerical solutions.,
- Lie groups.

**Edition Notes**

Statement | George W. Bluman, Sukeyuki Kumei. |

Series | Applied mathematical sciences ;, v. 81, Applied mathematical sciences (Springer-Verlag New York Inc.) ;, v. 81. |

Contributions | Kumei, Sukeyuki. |

Classifications | |
---|---|

LC Classifications | QA1 .A647 vol. 81, QA372 .A647 vol. 81 |

The Physical Object | |

Pagination | xiii, 412 p. : |

Number of Pages | 412 |

ID Numbers | |

Open Library | OL2188200M |

ISBN 10 | 0387969969 |

LC Control Number | 89006386 |

Symmetry methods have long been recognized to be of great importance for the study of the differential equations arising in mathematics, physics, engineering, and many other disciplines. The purpose of this book is to provide a solid introduction to those applications of Lie groups to differential equations that have proved to be useful in practice, including determination of symmetry groups 4/5(2). The Lie algebra approach to symmetries of integro-differential equations is not a new subject, and there is a quite extensive available literature [13][14] [15]. However, in contrast to the local.

Symmetries of DiﬀerentialEquations In this chapter we discuss the foundations and some applications of Lie’s theory of symmetry groups of diﬀerential equations. The basic inﬁnitesimal method for calculating symmetry groups is presented, and used to determine the general symmetry group of some particular diﬀerential equations of Size: KB. Symmetries in various forms pervade mathematics and physics. Globally, there are the symmetries of a homogenous space induced by the action of a Lie group. Locally, there are the infinitesimal symmetries induced by differential operators, including not only those of first order but of higher order too.

Symmetries in various forms pervade mathematics and physics. Globally, there are the symmetries of a homogenous space induced by the action of a Lie group. Locally, there are the infinitesimal symmetries induced by differential operators, including not only those of first order but of higher order. Description: This is an acessible book on the advanced symmetry methods for differential equations, including such subjects as conservation laws, Lie-Bäcklund symmetries, contact transformations, adjoint symmetries, Nöther's Theorem, mappings with some modification, potential symmetries, nonlocal symmetries, nonlocal mappings, and non-classical method. Of use to graduate students and .

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Differential equations as used here are equations which involve speeds, accelerations, and in general rates of change at each time or place. To understand what Bluman and Kumei (BK for short) do in everyday language, remember that an equation, such as E = m times c-squared, involves variables like E (energy), m (mass).Cited by: Symmetries and Differential Equations.

A major portion of this book discusses work which has appeared since the publication of the book Similarity Methods for Differential Equations, Springer-Verlag,by the first author and J.D.

Cole. The present book also includes a thorough and comprehensive treatment of Lie groups of tranformations and their various uses for solving ordinary and partial differential equations. In many branches of physics, mathematics, and engineering, solving a problem means solving a set of ordinary or partial differential equations.

Nearly all methods of constructing closed form solutions rely on symmetries. The emphasis in this text is on how to find and use the symmetries; this is supported by many examples and more than by: This book investigates the high degree of symmetry that lies hidden in integrable systems.

To that end, differential equations arising from classical mechanics, such as the KdV equation and the KP equations, are used here by the authors to introduce the notion of an infinite dimensional transformation group acting on spaces of integrable s: 2. Symmetries and Differential Equations.

A major portion of this book discusses work which has appeared since the publication of the book Similarity Methods for Differential Equations, Springer-Verlag,by the first author and J.D. Cole. Emphasis is placed on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries.

This book should be particularly suitable for physicists, applied mathematicians, and engineers. A major portion of this book discusses work which has appeared since the publication of the book Similarity Methods for Differential Equations, Springer-Verlag,by the first author and J.D. 6 Construction of Mappings Relating Differential Equations.- 7 Potential Symmetries.- References.- oclc\/\/a>> # Symmetries and.

Based on the third International Conference on Symmetries, Differential Equations and Applications (SDEA-III), this proceedings volume highlights recent important advances and trends in the applications of Lie groups, including a broad area of topics in interdisciplinary studies, ranging from mathematical physics to financial mathematics.

This book aims to coherently present applications of group analysis to integro-differential equations in an accessible way. The book will be useful to both physicists and mathematicians interested in general methods to investigate nonlinear problems using symmetries.

Differential and integro-differential equations, especially nonlinear, present. Symmetries and Differential Equations Chapter (PDF Available) in The Mathematical Gazette 74() January with 1, Reads How we measure 'reads'. Symmetries of Partial Differential Equations Conservation Laws — Applications — Algorithms.

Editors: Vinogradov, A.M. (Ed.) Free Preview. Buy this book eBook ,59 € price for Spain (gross) Buy eBook ISBN ; Digitally watermarked, DRM-free.

This book provides an introduction to the theory and application of the solution of differential equations using symmetries, a technique of great value in mathematics and the physical sciences. In many branches of physics, mathematics, and engineering, solving a problem means a set of ordinary or partial differential by: Symmetry Analysis of Differential Equations: An Introduction is an ideal textbook for upper-undergraduate and graduate-level courses in symmetry methods and applied mathematics.

The book is also a useful reference for professionals in science, physics, and engineering, as well as anyone wishing to learn about the use of symmetry methods in solving differential by: 2. Symmetry Methods for Differential Equations Symmetry is the key to solving differential equations.

There are many well- This book introduces applied mathematicians, engineers, and physicists to In order to understand symmetries of differential equations, it is helpful to consider symmetries of simpler objects. Roughly speaking, a.

Symmetries in various forms pervade mathematics and physics. Globally, there are the symmetries of a homogenous space induced by the action of a Lie group. Locally, there are the infinitesimal symmetries induced by differential operators, including not only those of first order but of higher order : Hardcover.

Classification of the symmetries of ordinary differential equations. Krause + and L. Michel Institut des Hautes Etudes Scientif~ques, Bures-sur-Yvette, France I Introduction. How can we make such a classification. One has to choose a group G acting on the set of ODE (ordinary differential equations).Cited by: 9.

The topic of this article is the symmetry analysis of differential equations and the applications of computer algebra to the extensive analytical calculations which are usually involved in it. The whole area naturally decomposes into two parts depending on whether ordinary or partial differential equations are considered.

We show how a symmetry may be applied to lower the order of an ordinary Cited by: Instead, a given differential equation is forced to reveal its symmetries, which are then used to construct exact solutions.

This book is a straightforward introduction to the subject, and is aimed at applied mathematicians, physicists, and by: In many branches of physics, mathematics, and engineering, solving a problem means solving a set of ordinary or partial differential equations. Nearly all methods of constructing closed form solutions rely on symmetries.

The emphasis in this text is on how to find and use the symmetries Price: $ Get this from a library. Symmetries and Differential Equations. [George W Bluman; Sukeyuki Kumei] -- A major portion of this book discusses work which has appeared since the publication of the book Similarity Methods for Differential Equations, Springer-Verlag,by the first author and J.D.

This book provides an introduction to the theory and application of the solution of differential equations using symmetries, a technique of great value in mathematics and the physical sciences. In many branches of physics, mathematics, and engineering, solving a problem means a set of ordinary or partial differential equations.

Nearly all methods of constructing closed form solutions rely on 5/5(1).Symmetry Analysis of Differential Equations: An Introduction is an ideal textbook for upper-undergraduate and graduate-level courses in symmetry methods and applied mathematics.

The book is also a useful reference for professionals in science, physics, and engineering, as well as anyone wishing to learn about the use of symmetry methods in.Key words. Higher symmetries, conservation laws, partial differential equations, infinitely prolonged equations, generating functions.

o. Introduction In this paper we present the basic notions and results from the general theory of local symmetries and conservation laws of partial differential equations.