Last edited by Akidal
Monday, April 27, 2020 | History

3 edition of Nonlinear symmetries and nonlinear equations found in the catalog.

Nonlinear symmetries and nonlinear equations

Giuseppe Gaeta

# Nonlinear symmetries and nonlinear equations

Written in English

Subjects:
• Differential equations, Nonlinear.,
• Symmetry (Physics),
• Mathematical physics.

• Edition Notes

The Physical Object ID Numbers Statement by Giuseppe Gaeta. Series Mathematics and its applications -- v.299 Pagination xix,258p. ; Number of Pages 258 Open Library OL22413055M ISBN 10 079233048X

Homotopy Analysis Method in Nonlinear Differential Equations - Ebook written by Shijun Liao. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Homotopy Analysis Method in Nonlinear Differential : Shijun Liao. partial differential equations (PDEs) invariant can be found in many books on this subject [8,11,12]. The key to ﬁnding a Lie group of symmetry transformations is the inﬁnitesimal generator of the group. In order to provide a bases of group generators one has to create and then to solve the so called determining system of equations (DSEs). I expect that KPZ equation is invariant under the non-linear symmetry, but I never checked. $\endgroup$ – Steven Mathey Oct 22 '15 at $\begingroup$ @WeatherReport Hm I'm not sure I agree with that, if the actions are the same before and after the transformation then the EOMs derived from those actions will be the same too.

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### Nonlinear symmetries and nonlinear equations by Giuseppe Gaeta Download PDF EPUB FB2

The study of (nonlinear) dift"erential equations was S. Lie's motivation when he created what is now known as Lie groups and Lie algebras; nevertheless, although Lie group and algebra theory flourished and was applied to a number of dift"erent physical situations -up to the point that a lot, if not most, of current fun­ damental elementary particles physics is actually (physical.

Buy Symmetries and Exact Solutions for Nonlinear Systems: Nonlinear symmetries and nonlinear equations book coefficients KdV and Boussinesq systems on FREE SHIPPING on qualified orders. This book is devoted to (1) search Lie and conditional (non-classical) symmetries of nonlinear RDC equations, (2) constructing exact solutions using the symmetries obtained, and (3) their applications for solving some biologically and physically motivated by: 7.

Lie point symmetries of Itô stochastic differential equations (SDEs) are considered. They correspond to Lie group transformations of the independent variable (time) and dependent variables, which preserve the differential form of the SDEs and properties of Brownian by: 1.

Nonlinear Symmetries and Nonlinear Equations And dynamical systems, book serves nonlinear symmetries studying, nevertheless, and then practice. Part I provides self-contained introduction type II Non-classical symmetries dimensions coincide with symmetries/10(74). This book is a collection of the papers published in the journal Symmetry within two Special Issues: Lie Theory and Its Applications and Lie and Conditional Symmetries and Their Applications for Solving.

Nonlinear Models, for which I served as the Guest Editor in – The book. adjoint symmetries [9,10,41] and (v) telescopic vector ﬁelds [40,42]. In the conventional Lie symmetry analysis, the invariance of differential equations. under one parameter Lie group of continuous transformations is investigated with point.

transformations alone. 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 approach to Cited by: phase-plane analysis describes nonlinear phenomena such as limit cycles and multiple equilibria of second-order systems in an efﬁcient manner.

The theory of differential equations has led to a highly developed stability theory for some classes of nonlinear systems. (Though, of course, an engineer cannot live by stability alone.) Functional.

Nonlinear Symmetries and Nonlinear Equations. [Giuseppe Gaeta] -- This book serves as an introduction to the use of nonlinear symmetries in studying, simplifying and solving nonlinear equations. Part I provides a self-contained introduction to the theory.

This text is an introduction to the use of nonlinear symmetries in the study solution of nonlinear equations. It outlines jet spaces and the geometry of differential equations, evolution problems, and dynamical systems, and looks at applications in equivariant dynamics and bifurcation theory.

This Nonlinear symmetries and nonlinear equations book is devoted to (1) search Lie and conditional (non-classical) symmetries of nonlinear RDC equations, (2) constructing exact solutions using the symmetries obtained, and (3) their applications for solving some biologically and physically motivated problems.

The book summarises the results derived by the authors during the last 10 years. Symmetries of nonlinear differential equations and linearisation Article (PDF Available) in Journal of Physics A General Physics 20(2) February with Reads How we measure 'reads'.

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 approach to.

Symmetries and Semi-invariants in the Analysis of Nonlinear Systems will be of interest to researchers and graduate students studying control theory, particularly with respect to nonlinear systems.

All the necessary background and mathematical derivations are related in detail but in a simple writing style that makes the book accessible in depth to readers having a standard knowledge of real.

The Lie-group formalism is applied to deduce the classical symmetries of the nonlinear heat equation, the diffusion-convection equation and the nonlinear wave equations. Some nonclassical. Bifurcation theory and nonlinear symmetries Let us now see what happens when symmetries are present (assuming the reader has some aquaintance with the application of group theory to differential equations, see [8, 12]).

We rewrite (1) as O .1, u.1) = 0 (10) DX .k,u) so that A: T (f3 x TA x (x A -> Tffl x by: 4. This book collects all known solutions to the nonlinear Schrödinger equation (NLSE) in one resource.

In addition, the book organizes the solutions by classifying and grouping them based on aspects and symmetries they possess. Although most of the solutions presented in this book have been derived elsewhere using various methods, the authors. Symmetries and singularity structures: integrability and chaos in nonlinear dynamical systems: proceedings of the workshop, Bharatidasan University, Tiruchirapalli, India, November December 2, Research reports in physics Lecture Notes in Physics: Authors: Muthusamy Lakshmanan, Muthiah Daniel: Editors: Muthusamy Lakshmanan, Muthiah.

Purchase Nonlinear Differential Equations - 1st Edition. Print Book & E-Book. ISBNBook Edition: 1. Abstract: Lie symmetry analysis is one of the powerful tools to analyze nonlinear ordinary differential equations.

We review the effectiveness of this method in terms of various symmetries. We present the method of deriving Lie point symmetries, contact symmetries, hidden symmetries, nonlocal symmetries, $\lambda$-symmetries, adjoint symmetries and telescopic vector fields of a second Author: M.

Senthilvelan, V. Chandrasekar, R. Mohanasubha. This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and elliptic equations.

Unlike comparable books that typically only use formal. Symmetries and Singularity Structures Integrability and Chaos in Nonlinear Dynamical Systems. Master Symmetries of Certain Nonlinear Partial Differential Equations.

On the Quantum Inverse Problem for a New Type of Nonlinear Schrödinger Equation for Alfven Waves in Plasma. Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing by: ture of these equations (e.g.

symmetries, conservation laws, and explicit solutions), and then turn to the analytic theory (e.g. existence and uniqueness, and asymptotic behaviour). The ﬁrst chapter is devoted entirely to ordinary diﬀerential equations (ODE).

One can view partial diﬀerential equations (PDE) such as the nonlinear. We review here the main properties of symmetries of separating hierarchies of nonlinear Schrödinger equations and discuss the obstruction to symmetry liftings from (n)particles to a higher number.

We argue that for particles with internal degrees of freedom, new multiparticle effects must appear at each particle-number : George Svetlichny.

Abstract. We examine the presence of general (nonlinear) time-independent Lie point symmetries in dynamical systems, and especially in bifurcation problems. A crucial result is that center manifolds are invariant under these symmetries: this fact, which may also Cited by: 7.

The radially symmetric nonlinear reaction–diffusion equation with gradient-dependent diffusivity is investigated. We obtain conditions under which the equations admit second-order conditional Lie–Bäcklund symmetries and first-order Hamilton–Jacobi sign-invariants which preserve both signs (≥0 and ≤0) on the solution manifold.

Nonlinear equations can often be approximated by linear ones if we only need a solution "locally," for example, only for a short period of time, or only for certain parameters. Understanding linear equations can also give us qualitative understanding about a more general nonlinear problem.

The problem of approximate symmetries of a class of nonlinear reaction-diffusion equations called Kolmogorov-Petrovsky-Piskounov (KPP) equation is comprehensively analyzed.

In order to compute the approximate symmetries, we have applied the method which was proposed by Fushchich and Shtelen () and fundamentally based on the expansion of the dependent variables in a perturbation : Mehdi Nadjafikhah, Abolhassan Mahdavi. This book is devoted to (1) search Lie and conditional (non-classical) symmetries of nonlinear RDC equations, (2) constructing exact solutions using the symmetries obtained, and (3) their applications for solving some biologically and physically motivated by: 7.

Lie symmetry method is performed for the nonlinear Jaulent-Miodek equation. We will find the symmetry group and optimal systems of Lie subalgebras. The Lie invariants associated with the symmetry generators as well as the corresponding similarity reduced equations are also pointed out.

And conservation laws of the J-M equation are presented with two steps: firstly, finding multipliers for Author: Mehdi Nadjafikhah, Mostafa Hesamiarshad. Some symmetries of the nonlinear heat and wave equations.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Nonlinear symmetries of finite dimensional dynamical systems are related to nonlinear normal forms and center manifolds in the neighbourhood of a singular point. Certain abstract results can be used algorithmically to construct the normal forms and/or the center manifold up to a given order in the perturbation expansion.

This book gives a comprehensive introduction to this technique. Ordinary and partial differential equations are studied with this approach. The book also covers nonlinear difference equations. The connections with Lie symmetries, the Painlevé property, first integrals and the Cartan equivalence method are discussed in detail.

We note here that the above equations are relations connecting the known point symmetries of the linear ODEs to symmetries of the nonlinear ODEs. Solving these coupled equations, one can obtain the symmetries for the nonlocal equation.

However, we find that the general solution of the above equation cannot be given for arbitrary forms of f and g. those, the Lie symmetries are considered as one of the most powerful technique for solving either partial differential equation or nonlinear coupled system of integro-differen-tial equation [22–28].

For a given k(u), the symmetries group of KP equation is investigated by many authors. Recently, the symme. In this paper we consider a damped externally excited Korteweg-de Vries (KdV) equation with a forcing term. We derive the classical Lie symmetries admitted by the equation. We then find that the damped externally excited KdV equation has some exact solutions which are periodic waves and solitary waves.

These solutions are derived from the solutions of a simple nonlinear ordinary differential. equations uses the knowledge of symmetries and conservation laws in connection with the scaling properties. The algorithms for symmetries and conservation laws are implemented in Mathe-matica and can be used to test the integrability of both nonlinear evolution equations and semi-discrete lattice equations.

A straightforward algorithm for the symbolic computation of higher-order sym-metries of nonlinear evolution equations and lattice equations is presented. The scaling properties of the evolution or lattice equations are used to determine the. —Nonclassical symmetries of the fourth-order nonlinear partial differential equation with dispersion and dissipation are obtained and are used as a basis for deriving new exact solutions that are invariant with respect to these symmetries.

The equation describes the. Nonlinear Differential Equations and Nonlinear Mechanics provides information pertinent to nonlinear differential equations, nonlinear mechanics, control theory, and other related topics.

This book discusses the properties of solutions of equations in standard form in the infinite time Edition: 1.Abraham-Shrauner and A. Guo, Hidden and nonlocal symmetries of nonlinear differential equations, in Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics, eds.

N. H. IbragimovM. by: 8.