Differential galois groups and representation of quivers for seismic models with constant hessian of square of slowness

Abstract

The trajectory of energy is modeled by the solution of the Eikonal equation, which can be solved by solving a Hamiltonian system. This system is amenable of treatment from the point of view of the theory of differential algebra. In particular, by Morales-Ramis theory, it is possible to analyze integrable Hamiltonian systems through the abelian structure of their variational equations. In this paper, we obtain the abelian differential Galois groups and the representation of the quiver, that allow us to obtain such abelian differential Galois groups, for some seismic models with constant Hessian of square of slowness, proposed in [20], which are equivalent to linear Hamiltonian systems with three uncoupled harmonic oscillators.