论文标题
在2曲面上的可整合磁性流动
Integrable magnetic geodesic flows on 2-surfaces
论文作者
论文摘要
我们研究了具有额外的第一积分的2个曲面上的磁性测量流，该集成量与固定能级无关的哈密顿量。考虑以下两种情况：当Momenta积分中存在二次的情况时，以及与线性分子和分母的Momenta积分中有理理性的情况。在这两种情况下，都出现了某些半汉密尔顿PDES系统。在本文中，我们对这些系统构建精确的解决方案（通常是本地的）：在第一种情况下，通过广义Hodograph方法，在第二种情况下通过Legendre Transformation和变量分离方法。
We study the magnetic geodesic flows on 2-surfaces having an additional first integral which is independent of the Hamiltonian at a fixed energy level. The following two cases are considered: when there exists a quadratic in momenta integral, and also the case of a rational in momenta integral with a linear numerator and denominator. In both cases certain semi-Hamiltonian systems of PDEs appear. In this paper we construct exact solutions (generally speaking, local ones) to these systems: in the first case via the generalized hodograph method, in the second case via the Legendre transformation and the method of separation of variables.
