论文标题
painlevéIII方程的非亚伯式Toda格子和类似物
Non-Abelian Toda lattice and analogs of Painlevé III equation
论文作者
论文摘要
在可集成的模型中，较高对称性的固定方程是与动力学一致的减少的主要来源之一。我们将此方法应用于非亚洲二维TODA晶格。结果表明，最简单的较高流量的固定方程已经给出了一个非平凡的非自主约束，该约束将TODA晶格降低到泵送麦克斯韦的非亚洲类似物-Bloch方程。 Toda晶格本身被解释为作用于该系统解决方案的自动 - bäcklund转换。进一步的自相似减少导致PainlevéIII方程的非亚伯类似物。
In integrable models, stationary equations for higher symmetries serve as one of the main sources of reductions consistent with dynamics. We apply this method to the non-Abelian two-dimensional Toda lattice. It is shown that already the stationary equation of the simplest higher flow gives a non-trivial non-autonomous constraint that reduces the Toda lattice to a non-Abelian analog of the pumped Maxwell--Bloch equations. The Toda lattice itself is interpreted as an auto-Bäcklund transformation acting on the solutions of this system. Further self-similar reduction leads to non-Abelian analogs of the Painlevé III equation.
