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Tuesday, July 28, 2020 | History

5 edition of Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics (Mathematics and Its Applications) found in the catalog.

Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics (Mathematics and Its Applications)

by W.I. Fushchich

  • 184 Want to read
  • 40 Currently reading

Published by Springer .
Written in English

    Subjects:
  • Calculus & mathematical analysis,
  • Mathematics for scientists & engineers,
  • Science,
  • Group Theory,
  • Symmetry,
  • Numerical Solutions Of Differential Equations,
  • Numerical solutions,
  • Science/Mathematics,
  • Mathematical Analysis,
  • Mathematics : Group Theory,
  • Mathematics : Mathematical Analysis,
  • Science / Mathematical Physics,
  • Differential equations, Hyperb,
  • Differential equations, Hyperbolic,
  • Differential equations, Parabo,
  • Differential equations, Parabolic,
  • Mathematical Physics

  • The Physical Object
    FormatHardcover
    Number of Pages460
    ID Numbers
    Open LibraryOL7807138M
    ISBN 100792321464
    ISBN 109780792321460

    I am looking for an up to date book on the symmetry approach to finding exact solutions to linear/non linear ordinary/partial systems of differential equations. By modern approach I mean with the use of symmetry analysis. It would be preferable to have a book geared towards applications in physics. Lie symmetry analysis and dynamical system method is a feasible approach to dealing with exact explicit solutions to nonlinear PDEs and systems, (see, e.g., [7]–[12]). Liu et al derived the symmetries, bifurcations and exact explicit solutions to the KdV equation by using Lie symmetry analysis and the dynamical system method [13]. The STO.

    and construction of exact solutions of nonlinear differential equations. Moreover, the latest trends in symmetry analysis, such as conditional symmetry, potential symmetries, discrete symmetries and differential geometry approach to symmetry analysis were represented efficiently. In addition, important branches of symmetry analysis such as repre-.   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 Reviews: 2.

    the Lie symmetry analysis. Algebraic properties of higher order SOsare investigated and used to con-struct exact solutions of the linear and related nonlinear Schr¨odinger equa-tions. We propose a new method to generate extended families of exact solutions by using both the conditional symmetries8,12−14 and higher order SOs. In this work, Lie symmetry analysis for the time fractional third-order evolution (TOE) equation with Riemann–Liouville (RL) derivative is analyzed. We transform the time fractional TOE equation to nonlinear ordinary differential equation (ODE) of fractional order using its Lie point symmetries with a new dependent variable.


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Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics (Mathematics and Its Applications) by W.I. Fushchich Download PDF EPUB FB2

Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics. Authors (view affiliations) A brief account of the main ideas of the book is presented in the Introduction. The book is largely based on the authors' works [, 7**,23*, 24*] carried out in the Institute of Mathematics, Academy of.

Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics W. Fushchich, W. Shtelen, N. Serov (auth.) 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.

A brief account of the main ideas of the book is presented in the Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics. Authors: Fushchich, W.I., Shtelen, W.M., Serov, N.I. Free Preview. Buy this book eBookThe book provides an overview of the current status of theoretical-algebraic methods in relation to linear and nonlinear multidimensional equations in mathematical and theoretical physics that are invariant with respect to the Poincare and Galilean groups and the wider Lie groups.

Particular attention is given to the construction, in explicit form, of wide classes of accurate solutions to Author: Vil'gel'm. Fushchich, Vladimir M.

Shtelen, Nikolai I. Serov. Lie symmetry analysis and exact solutions of the quasigeostrophic two-layer problem Fushchych, W. and Popovych, R. O., “ Symmetry reduction and exact solutions of the Navier–Stokes equations,” J.

Nonlinear Math. Phys. 1(1 Katkov, V. L., “ A class of exact solutions of the equation for the forecast of the geopotential,” Izv Cited by:   Abstract: The authors give a detailed information about symmetry (Lie, non-Lie, conditional) of nonlinear PDEs for spinor, vector and scalar fields; using advanced methods of group-theoretical, symmetry analysis construct wide families of classical solutions of the nonlinear Dirac, Yang-Mills, Maxwell-Dirac, Dirac-d'Alembert, d'Alembert-Hamilton equations; expound a new symmetry.

'This new book by Peter Hydon is eminently suitable for advanced undergraduates and beginning postgraduate students Overall I thoroughly recommend this book and believe that it will be a useful textbook for introducing students to symmetry methods for differential equations.' Source: Journal of Nonlinear Mathematical Physics.

The purpose of this book is to provide the reader with a comprehensive introduction to the applications of symmetry analysis to ordinary and partial differential equations. The theoretical background of physics is illustrated by modem methods of computer algebra. The presentation of the material in the book is based on Mathematica note­ books.

() Symmetry analysis and group-invariant solutions to inhomogeneous nonlinear diffusion equation. Communications in Nonlinear Science and Numerical Simulation() Conditional Lie–Bäcklund symmetry, second-order differential constraint and direct reduction of diffusion systems.

The main purpose of this paper is to present a new approach to achieving analytical solutions of parameter containing fractional-order differential equations. Using the nonlinear self-adjoint notion, approximate solutions, conservation laws and symmetries of these equations are also obtained via a new formulation of an improved form of the Noether’s theorem.

Fushchych and N. Serov, “Conditional invariance and exact solutions of the Boussinesq equation,” in: Symmetry and Solutions of Nonlinear Equations of Mathematical Physics (in Russian) (Inst. of Math., Acad. Sci. of Ukraine, Kiev, ), pp. 96– Symmetry analysis and exact solutions of equations of nonlinear mathematical physics.

Dordrecht ; Boston: Kluwer Academic Publishers, © (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: V I. It appears that cases of exact solutions of differential equations are based on the use of symmetries of these equations with respect to certain transformation.

Symmetry analysis is one of the systematic and accurate ways to obtain solutions of differential equations. The book provides an overview of the current status of theoretical-algebraic methods in relation to linear and nonlinear multidimensional equations in mathematical and theoretical physics that are.

Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics (Mathematics and Its Applications) rd Edition by W.I. Fushchich (Author), W.M.

Shtelen (Author), N.I. Serov (Author) & 0 moreCited by: exact solutions of nonlinear dieren system, ” Journal of Mathematical Physics,v o l.4 9,n a new solution is obtained by using a given solution of the equation.

The symmetry is also. In this paper, a complete Lie symmetry analysis is performed for a nonlinear Fokker-Planck equation for growing cell populations. Moreover, an optimal system of one-dimensional subalgebras is constructed and used to find similarity reductions and invariant solutions.

A new power series solution is constructed via the reduced equation, and its convergence is proved. The group-theoretical analysis is known to be used for the construction of exact solutions of a number of linear and nonlinear equations of mathematical physics [1, 2].

One of the most efficient methods for the obtaining of explicit solutions is the method of group reduction [ 1 – 11 ].

The time-fractional nonlinear Schrödinger equation with parabolic law nonlinearity is studied. Under the travelling wave transformations, Schrödinger. Broadly, my research lies in nonlinear differential equations, symmetry analysis, integrability and solitons, and mathematical physics.

My interests in nonlinear differential equations center on applications of symmetry analysis and conservation laws to the study of PDEs, particularly nonlinear wave equations and soliton equations, as well as ODEs connected with exact solutions through.

We consider the Cauchy problem of the nonlinear Schrödinger equation with magnetic effect, and prove global existence of smooth solutions and decay estimates for suitably small initial data.

The key step in our analysis is to exploit the null structures for the phases, which allow us to close our argument in the framework of space-time resonance method.Let math id="M1">\begin{document}$ a>0,b>0 $\end{document}math> and math id="M2">\begin{document}$ V.DANIEL J.

ARRIGO, PhD, is Professor in the Department of Mathematics at the University of Central author of over 30 journal articles, his research interests include the construction of exact solutions of PDEs; symmetry analysis of nonlinear PDEs; and solutions to physically important equations, such as nonlinear heat equations and governing equations modeling of granular .