Abstract
A family of new PDE systems of one-dimensional nonlinear elastodynam-ics, which are nonlocally related to the classical Lagrange and Euler formulations, is derived. These new PDE systems provide alternative equivalent descriptions of the one-dimensional nonlinear elasticity model. In particular, nonlocally related systems are used to find nonlocal symmetries of the Euler system for various forms of constitutive and loading functions. Examples of new dynamical solutions arising as group invariant solutions with respect to such nonlocal symmetries are constructed. Another application of nonlocally related systems considered in this paper is the construction of nonlocal conservation laws. Examples of nonlocal conservation laws are derived for several classes of stress-strain relations and loading functions.KeywordsNonlinear ElasticityInvariant SolutionPotential SystemLagrange SystemEuler SystemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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