Using Lie symmetry methods for differential equations we have investigated the symmetries of a Lagrangian for a plane symmetric static spacetime. Perturbing this Lagrangian we explore its approximate symmetries. It has a non-trivial first-order approximate symmetry.

"Optimal systems" of similarity solutions of a given system of nonlinear partial (integro-)differential equations which admits a finite-dimensional Lie point symmetry group G are an effective systematic means to classify these group-invariant solutions since every other such solution can be derived from the members of the optimal systems. The classification problem for the similarity solutions ...

where ξ is a real-valued function and η is a 2 × 2 matrix complex-valued function, a Lie symmetry of system (1) if commutation relation [L,X] = R(x)L, (4) holds with some 2× 2 matrix function R(x) (for details, see, e.g., Ref. [3]). A simple computation shows that if X is a Lie symmetry of system (1), then an operator X + r(x)L with a smooth function r(x) is its Lie symmetry as well. Hence we c...