TY - JOUR

T1 - Differential galois groups and representation of quivers for seismic models with constant hessian of square of slowness

AU - Acosta-Humánez, Primitivo

AU - Giraldo, Hernán

AU - Piedrahita, Carlos

PY - 2017/8/1

Y1 - 2017/8/1

N2 - © 2017 Pushpa Publishing House, Allahabad, India. 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.

AB - © 2017 Pushpa Publishing House, Allahabad, India. 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.

U2 - 10.17654/MS102030599

DO - 10.17654/MS102030599

M3 - Article

SP - 599

EP - 623

JO - Far East Journal of Mathematical Sciences

JF - Far East Journal of Mathematical Sciences

SN - 0972-0871

ER -