Group theoretic methods for approximate invariants and Lagrangians for some classes of y″+εF(t)y′+y=f(y,y′) |
| |
Authors: | T FerozeAH Kara |
| |
Institution: | a Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan b Department of Mathematics, University of the Witwatersrand, Centre for Differential Equations, Continuum Mechanics and Applications, Private Bag 3, Wits 2050, Johannesburg, South Africa |
| |
Abstract: | Some recent results on the Lie symmetry generators of equations with a small parameter and the relationship between symmetries and conservation laws for such equations are used to construct first integrals and Lagrangians for autonomous weakly non-linear systems, y″+εF(t)y′+y=f(y,y′). An adaptation of a theorem that provides the point symmetry generators that leave the invariant functional involving a Lagrangian for such equations is presented. A detailed example to illustrate the method is given (and other examples are discussed). The (approximate) symmetry generators, invariants and Lagrangians maintain the perturbation order of the ‘small parameter’ stipulated in the equation — first order in this case. |
| |
Keywords: | Approximate symmetries First integrals Invariants Lagrangians |
本文献已被 ScienceDirect 等数据库收录! |
|