We prove a DuBois–Reymond necessary optimality condition and a Noether symmetry theorem to the recent quantum variational calculus of Cresson. The results are valid for problems of the calculus of variations with functionals defined on sets of nondifferentiable functions. As an application, we obtain a constant of motion for a linear Schrödinger equation. AMS Subject Classifications: 49K05, 49S...

The conservation of helicity in ideal barotropic fluids is discussed from a group theoretical point of view. A new symmetry group is introduced i.e. the alpha group of translations. It is proven via the Noether theorem that this group generates helicity conservation.

An infinite sequence of commuting nonpolynomial contact symmetries of the two-dimensional minimal surface equation is constructed. Local and nonlocal conservation laws for n-dimensional minimal area surface equation are obtained by using the Noether identity. Introduction. In this paper, we analyze the symmetry properties of the Euler equation