Continuous symmetries of Lagrangians and exact solutions of discrete equations

Details Continuous symmetries of Lagrangians and exact solutions of discrete equations Continuous symmetries of Lagrangians and exact solutions of discrete equations

2003-07-23

arxiv.org/abs/nlin/0307042v1

J. Math. Phys. 45 (2004), no. 1, 336-359

Nonlinear Sciences

Exactly Solvable and Integrable Systems

31 pages, submitted to Journal of Mathematical Physics

Scientific paper

10.1063/1.1625418

One of the difficulties encountered when studying physical theories in discrete space-time is that of describing the underlying continuous symmetries (like Lorentz, or Galilei invariance). One of the ways of addressing this difficulty is to consider point transformations acting simultaneously on difference equations and lattices. In a previous article we have classified ordinary difference schemes invariant under Lie groups of point transformations. The present article is devoted to an invariant Lagrangian formalism for scalar single-variable difference schemes. The formalism is used to obtain first integrals and explicit exact solutions of the schemes. Equations invariant under two- and three- dimensional groups of Lagrangian symmetries are considered.

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