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Author : W. I. Fushchich
Release : 2014-01-15
Genre :
Kind : eBook
Book Rating : 997/5 ( reviews)
Book Synopsis Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics by : W. I. Fushchich
Download or read book Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics written by W. I. Fushchich. This book was released on 2014-01-15. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vilʹgelʹm Ilʹich Fushchich
Release : 1993-02-28
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics by : Vilʹgelʹm Ilʹich Fushchich
Download or read book Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics written by Vilʹgelʹm Ilʹich Fushchich. This book was released on 1993-02-28. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an account of the current state of algebraic-theoretic methods as applied to linear and nonlinear multidimensional equations of mathematical and theoretical physics. Equations are considered that are invariant under Euclid, Galilei, Schrödinger, Poincaré, conformal, and some other Lie groups, with special emphasis being given to the construction of wide classes of exact solutions of concrete nonlinear partial differential equations, such as d'Alembert, Liouville, Monge-Ampère, Hamilton-Jacobi, eikonal, Schrödinger, Navier-Stokes, gas dynamics, Dirac, Maxwell-Dirac, Yang-Mills, etc. Ansätze for spinor, as well as scalar and vector fields are described and formulae for generating solutions via conformal transformations are found explicitly for scalar, spinor, vector, and tensor fields with arbitrary conformal degree. The classical three-body problem is considered for the group-theoretic point of view. The symmetry of integro-differential equations is also studied, and the method of finding final nonlocal transformations is described. Furthermore, the concept of conditional symmetry is introduced and is used to obtain new non-Lie Ansätze for nonlinear heat and acoustic equations. The volume comprises an Introduction, which presents a brief account of the main ideas, followed by five chapters, appendices, and a comprehensive bibliography. This book will be of interest to researchers, and graduate students in physics and mathematics interested in algebraic-theoretic methods in mathematical and theoretical physics.
Author : Gangwei Wang
Release : 2024-08-13
Genre : Science
Kind : eBook
Book Rating : 095/5 ( reviews)
Book Synopsis Symmetry and Exact Solutions of Nonlinear Mathematical Physics Equations by : Gangwei Wang
Download or read book Symmetry and Exact Solutions of Nonlinear Mathematical Physics Equations written by Gangwei Wang. This book was released on 2024-08-13. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear problems, originating from applied science that is closely related to practices, contain rich and extensive content. It makes the corresponding nonlinear models also complex and diverse. Due to the intricacy and contingency of nonlinear problems, unified mathematical methods still remain far and few between. In this regard, the comprehensive use of symmetric methods, along with other mathematical methods, becomes an effective option to solve nonlinear problems.
Author : W.I. Fushchich
Release : 2013-03-14
Genre : Science
Kind : eBook
Book Rating : 985/5 ( reviews)
Book Synopsis Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics by : W.I. Fushchich
Download or read book Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics written by W.I. Fushchich. This book was released on 2013-03-14. Available in PDF, EPUB and Kindle. Book excerpt: by spin or (spin s = 1/2) field equations is emphasized because their solutions can be used for constructing solutions of other field equations insofar as fields with any spin may be constructed from spin s = 1/2 fields. A brief account of the main ideas of the book is presented in the Introduction. The book is largely based on the authors' works [55-109, 176-189, 13-16, 7*-14*,23*, 24*] carried out in the Institute of Mathematics, Academy of Sciences of the Ukraine. References to other sources is not intended to imply completeness. As a rule, only those works used directly are cited. The authors wish to express their gratitude to Academician Yu.A. Mitropoi sky, and to Academician of Academy of Sciences of the Ukraine O.S. Parasyuk, for basic support and stimulation over the course of many years; to our cowork ers in the Department of Applied Studies, LA. Egorchenko, R.Z. Zhdanov, A.G. Nikitin, LV. Revenko, V.L Lagno, and I.M. Tsifra for assistance with the manuscript.
Author : Sergey V. Meleshko
Release : 2006-06-18
Genre : Technology & Engineering
Kind : eBook
Book Rating : 657/5 ( reviews)
Book Synopsis Methods for Constructing Exact Solutions of Partial Differential Equations by : Sergey V. Meleshko
Download or read book Methods for Constructing Exact Solutions of Partial Differential Equations written by Sergey V. Meleshko. This book was released on 2006-06-18. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.
