Conformal Invariance of Higher-Order Lagrange Systems by Lie Point Transformation

Abstract

Conformal invariance and conserved quantities for a higher-order Lagrange system by Lie point transformation of groups are studied. The differential equation of motion for the higher-order Lagrange system is introduced. The definition of conformal invariance for the system together with its determining equations and conformal factor are provided. The necessary and sufficient condition that the system's conformal invariance would be Lie symmetry by the infinitesimal one-parameter point transformation group is deduced. The conserved quantity of the system is derived using the structural equation satisfied by the gauge function. An example of a higher-order mechanical system is offered to illustrate the application of the result.

Dark Sharma–Tasso–Olver Equations and Their Recursion Operators

“…Huang and Cai obtained the analytic solution of the STO equation by the homotopy analysis method. [12] By applying the fermionization approach, three simple super-symmetric extensions of the STO equation are obtained. [13] As we all know, symmetry analysis plays an important role in nonlinear mathematical physics.…”