Differential galois groups and representation of quivers for seismic models with constant hessian of square of slowness
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Fecha
2017
Autores
Acosta-Humánez, Primitivo
Giraldo, Hernán
Piedrahita, Carlos
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Editor
Pushpa Publishing House
Resumen
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.
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Palabras clave
Differential Galois theory, Eikonal equation, Hamilton equation, Helmholtz equation, High frequency approximation, Morales-Ramis theory, Ray theory, Representations of quivers