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Wednesday, May 20, 2020 | History

9 edition of **Symmetries and conservation laws for differential equations of mathematical physics** found in the catalog.

- 7 Want to read
- 21 Currently reading

Published
**1999**
by American Mathematical Society in Providence, R.I
.

Written in English

- Differential equations -- Numerical solutions.,
- Symmetry.,
- Conservation laws (Mathematics),
- Mathematical physics.

**Edition Notes**

Includes bibliographical references (p. 323-328) and index.

Other titles | Symmetries and conservation laws |

Statement | A.V. Bocharov ... [et al.] ; I.S. Krasilʹshchik (editor) ... A.M. Vinogradov (editor) ; [translated from the Russian by A.M. Verbovetsky and I.S. Krasilʹshchik]. |

Series | Translations of mathematical monographs,, v. 182 |

Contributions | Bocharov, A. V., Krasilʹshchik, I. S., Vinogradov, A. M. |

Classifications | |
---|---|

LC Classifications | QC20.7.D5 S5613 1999 |

The Physical Object | |

Pagination | xiv, 333 p. : |

Number of Pages | 333 |

ID Numbers | |

Open Library | OL389087M |

ISBN 10 | 082180958X |

LC Control Number | 98053018 |

Abstract This book is devoted to the analysis of old (classical) and new (non-Lie) symmetries of the fundamental equations of quantum mechanics and classical field theory, and to the classification and algebraic-theoretical deduction of equations of motion of arbitrary spin particles in both Poincaré invariant approach. 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.

This book presents developments in the geometric approach to nonlinear partial differential equations (PDEs). The expositions discuss the main features of the approach, and the theory of symmetries and the conservation laws based on it. The book combines rigorous mathematics with concrete examples. The concept of sub-symmetry of a differential system was introduced in [], where it was shown that a sub-symmetry is a considerably more powerful tool than a regular symmetry with regard to deformation of conservation this paper, we study the nature of a correspondence between sub-symmetries and conservation laws of a differential by: 1.

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. In Lie Symmetry Analysis of Fractional Differential Equations the authors try to answer this vital question by analyzing different aspects of fractional Lie symmetries and related conservation laws. Finding the exact solutions of a given fractional partial differential equation is not an easy task, but is one that the authors seek to grapple.

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The expositions discuss the main features of the approach, and the theory of symmetries and the conservation laws based on it. The book combines rigorous mathematics with concrete examples. Nontraditional topics, such as the theory of nonlocal symmetries and cohomological theory of conservation laws, are also : I.

Krasilshchik and A. Vinogradov. Buy Symmetries of Partial Differential Equations: Conservation Laws ― Applications ― Algorithms on FREE SHIPPING on qualified orders. In the case of one PDE with two independent variables the association of symmetries with conservation laws allows us to apply a double reduction method which leads from a qth order PDE to an ordinary differential equation (ODE) of order q Recently this method has been generalized and applied to (2 + 1) wave by: Partial differential equations in classical mathematical physics / Isaak Rubinstein, Lev Rubinstein.

QC D5 R83 Symmetries and conservation laws for differential equations of mathematical physics / A.V. Bocharov. 2 The authors of these issues involve not only mathematicians, but also speci alists in (mathematical) physics and computer sciences. So here the reader will find different points of view and approaches to the considered field.

Symmetries and conservation laws of difference equations Article in Theoretical and Mathematical Physics (2) August with 9 Reads How we measure 'reads'.

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. 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.

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 conservation laws for the compacton equation and the compacton equation were constructed in by utilizing the multiplier approach. In [ 4 ], only multipliers of the form were considered since, according to the authors, the higher order multipliers determining equations are too complicated and cannot be separated by: A.

C., Symbolic Computation of Nonlocal Symmetries and Nonlocal Conservation Laws of Partial Differential Equations Using the GeM Package for Maple, Similarity and Symmetry Methods, Lecture Notes in Applied and Computational Mechan Springer, Equations on curved manifolds display interesting prop-erties in a number of ways.

In particular, the symmetries and, therefore, the conservation laws reduce depending on how curved the manifold is. Get this from a library. Symmetries and conservation laws for differential equations of mathematical physics.

[A V Bocharov; I S Krasilʹshchik; A M Vinogradov;] -- This book presents developments in the geometric approach to nonlinear partial differential equations (PDEs).

The expositions discuss the main features of the approach, and the theory of symmetries. Conservation laws play a vital role in the reduction and solution process of the differential equations. It is well known that the integrability of the differential equations is strongly related to the existence of conservation laws.

Conservation laws are used for existence, uniqueness and stability analysis and for the development of numerical methods. Conservation laws are fomulated for systems of differential equations by using symmetries and adjoint symmetries, and an application to systems of evolution equations is made, together with illustrative examples.

The formulation does not require the existence of a Lagrangian for a given system, and the presented examples include computations of conserved densities for the heat equation Cited by: Higher symmetries, conservation laws, partial differential equations, infinitely prolonged equations, generating functions.

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.

AbstractIn this paper, Lie symmetry analysis is performed for the equation derived from $(2+1)$-dimensional higher order Broer-Kaup equation. Meanwhile, the optimal system and similarity reductions based on the Lie group method are obtained.

Furthermore, the conservation law is studied via the Ibragimov’s : Hengtai Wang, Huiwen Chen, Zigen Ouyang, Fubin Li. Symmetries and conservation laws for differential equations of mathematical physics. [A V Bocharov; I S Krasilʹshchik; A M Vinogradov;] Higher Symmetries -- Ch.

Conservation Laws -- Ch. Nonlocal Symmetries -- App. From Symmetries of Partial Differential Equations Towards Secondary (\"Quantized\"). 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.

These notes present numerical methods for conservation laws and related time dependent nonlinear partial differential equations. The focus is on both simple scalar problems as. Symmetry Analysis and Conservation Laws of a Generalized Two-Dimensional Nonlinear KP-MEW Equation Khadijo Rashid Adem 1 and Chaudry Masood Khalique 1 1 International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag XMmabathoSouth Cited by:.

In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation.

A family of particular transformations may be continuous (such as rotation of a circle) or discrete (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon).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: Numerical methods for conservation laws and related equations.

These notes present numerical methods for conservation laws and related time dependent nonlinear partial differential equations. The focus is on both simple scalar problems as well as multi .