关于Lam {é}方程多分量推广的解
On the solutions of multicomponent generalizations of the Lam{é} equation
摘要：
我们描述了一类奇异的解决方案的多组分类似物的Lam {é}方程，产生的椭圆Calogero-Moser系统的粒子携带自旋1/2的运动方程。在特殊的耦合常数值下，我们提出了一种新的方法，该方法可以得到具有两个任意参数的亚纯解。它们被量子化后的要求的规则性的波函数的超平面上的粒子满足和施加周期性的边界条件。我们还发现额外的运动积分的三粒子系统的耦合常数的任意值与哈密尔顿交换。
英文摘要：
We describe a class of the singular solutions to the multicomponent analogs of the Lam{é} equation, arising as equations of motion of the elliptic Calogero--Moser systems of particles carrying spin 1/2. At special value of the coupling constant we propose the ansatz which allows one to get meromorphic solutions with two arbitrary parameters. They are quantized upon the requirement of the regularity of the wave function on the hyperplanes at which particles meet and imposing periodic boundary conditions. We find also the extra integrals of motion for three-particle systems which commute with the Hamiltonian for arbitrary values of the coupling constant.
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