### NON-STANDARD HIGHER-ORDER G -STRAND PARTIAL DIFFERENTIAL EQUATIONS ON MATRIX LIE ALGEBRA

#### Abstract

Let G be a Lie group and g(t, s) :RXR $\rightarrow$ G be its corresponding map where t and s are independent variables. A G -strand gives rise to dynamical equations for a map RXR into G

that follows from the standard Hamilton's principle. It is believed that a good number of important dynamical equations arising in different fields of sciences can be written as the Euler-Poisson equations on a matrix Lie algebra g of G . This picture was extended in literature to the higher-order derivatives case through different contexts in particular when the original configuration space is a configuration manifold Q on which a Lie group G acts appropriately. The goal of this paper is to extend G -strand equations on matrix Lie algebra to the higher-order derivatives case through a different approach and more precisely by means of non-standard Lagrangians where higher-order derivatives occur naturally although the Lagrangian holds 1st order derivative terms. Some consequences are discussed accordingly.

that follows from the standard Hamilton's principle. It is believed that a good number of important dynamical equations arising in different fields of sciences can be written as the Euler-Poisson equations on a matrix Lie algebra g of G . This picture was extended in literature to the higher-order derivatives case through different contexts in particular when the original configuration space is a configuration manifold Q on which a Lie group G acts appropriately. The goal of this paper is to extend G -strand equations on matrix Lie algebra to the higher-order derivatives case through a different approach and more precisely by means of non-standard Lagrangians where higher-order derivatives occur naturally although the Lagrangian holds 1st order derivative terms. Some consequences are discussed accordingly.

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