On applications of Maupertuis-Jacobi correspondence for Hamiltonians   $F(x,|p|)$ in some 2-D stationary semiclassical problems
  We make use of the Maupertuis -- Jacobi correspondence, well known in Classical Mechanics, to simplify 2-D asymptotic formulas based on Maslov's canonical operator, when constructing Lagrangian manifolds invariant with respect to phase flows for Hamiltonians of the form $F(x,|p|)$. As examples we consider Hamiltonians coming from the Schr\"odinger equation, the 2-D Dirac equation for graphene and linear water wave theory. 
S.Dobrokhotov, D.Minenkov (A.Ishlinskii Institute for Problems in   Mechanics Russian Academy of Sciences and Moscow institu...
math-ph math.MP