Transformations of Ordinary Differential Equations: Local and Nonlocal Symmetries

نویسنده

  • Lev M. BERKOVICH
چکیده

The brief review of new methods of factorization, autonomization and exact linearization of the ordinary differential equations is represented. These methods along with the method of the group analysis based on using both point and nonpoint, local and nonlocal transformations are effective tools for study of nonlinear autonomous and nonautonomous dynamical systems. Thus a scope of exactly solvable problems of the Nonlinear analysis is extended.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

λ−Symmetries and linearization of ordinary differential equations through nonlocal transformations ?

A recent study (Muriel and Romero (2010a)) on the linearization of ordinary differential equations through generalized Sundman transformations suggests considering the problem of linearization through nonlocal transformations from the point of view of the λ−symmetries admitted by the equation and their associated first integrals. The systematic methods to calculate λ−symmetries and associated f...

متن کامل

Nonlocal symmetries of a class of scalar and coupled nonlinear ordinary differential equations of any order

In this paper we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to linear ODEs through nonlocal relations. The procedure makes use of the Lie point symmetries of the linear ODEs and the nonlocal connection to deduce the nonlocal symmetries of the corresponding nonlinear ODEs. Using thes...

متن کامل

Reduction of Differential Equations by Lie Algebra of Symmetries

The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...

متن کامل

Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations

This paper studies relationships between the order reductions of ordinary differential equations derived by the existence of λ-symmetries, telescopic vector fields and some nonlocal symmetries obtained by embedding the equation in an auxiliary system. The results let us connect such nonlocal symmetries with approaches that had been previously introduced: the exponential vector fields and the λ-...

متن کامل

Nonlocal Bending Analysis of Bilayer Annular/Circular Nano Plates Based on First Order Shear Deformation Theory

In this paper, nonlinear bending analysis of bilayer orthotropic annular/circular graphene sheets is studied based on the nonlocal elasticity theory. The equilibrium equations are derived in terms of generalized displacements and rotations considering the first-order Shear deformation theory (FSDT). The nonlinear governing equations are solved using the differential quadrature method (DQM) whic...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1989