微分伽罗瓦群与慢度平方为常数的Hessian地震模型的箭图表示
Differential Galois Groups and Representation of Quivers for Seismic Models with Constant Hessian of Square of Slowness
摘要：
能量的轨迹由Eikonal方程的解来模拟，Eikonal方程可以通过求解哈密顿系统来求解。这个系统是服从处理的角度来看，微分代数的理论。特别地，通过Morales-Ramis理论，可以通过其变分方程的阿贝尔结构来分析可积哈密顿系统。本文给出了Cerveny在2001年提出的具有慢度平方常数Hessian的地震模型的Abel微分Galois群及其表示，这些地震模型等价于具有三个非耦合谐振子的线性Hamilton系统.
英文摘要：
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 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 Cerveny 2001, which are equivalent to linear Hamiltonian systems with three uncoupled harmonic oscillators.
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