标题： 现实条件下的正弦戈登方程和有限相空间中的拟周期解 显示英文标题

标题： Reality conditions for sine-Gordon equation and quasi-periodic solutions in finite phase spaces

摘要： sine-Gordon 方程的拟周期解可以用$\wp_{1,2g-1}$函数来表示，并且现实条件被完全确定。 这一新结果导致了非线性波解的计算和图形表示。 详细介绍了通过代数几何积分获得有限带解的方法，以及在$\mathrm{SU}(2)$的环群余伴随轨道上构造 sine-Gordon 层次结构的方法。 显示英文摘要

摘要： Quasi-periodic solutions of the sine-Gordon equation are expressed in terms of $\wp_{1,2g-1}$-function, and reality conditions are completely determined. This new result leads to computation and graphical representation of non-linear wave solutions. A way of obtaining finite-gap solutions by means of algebro-geometric integration is exposed in detail, as well as the construction of the sine-Gordon hierarchy on coadjoint orbits of the loop group of $\mathrm{SU}(2)$.