标题： 麦克金的变换用于三阶算子 显示英文标题

标题： Mc'Kean's transformation for 3-rd order operators

摘要： 我们考虑一个非自伴的三阶算子$(y''+py)'+py'+qy$，其系数为 1-周期的$p,q$。这个算子是圆上良好 Boussinesq 方程的 Lax 对中的 L 算子。1981 年，McKean 引入了一个变换，将该算子的谱问题转化为一个与能量解析相关的势函数的 Hill 算子的谱问题。在本文中，我们研究这个变换。 显示英文摘要

摘要： We consider a non-self-adjoint third order operator $(y''+py)'+py'+qy$ with 1-periodic coefficients $p,q$. This operator is the L-operator in the Lax pair for the good Boussinesq equation on the circle. In 1981, McKean introduced a transformation that reduces the spectral problem for this operator to a spectral problem for the Hill operator with a potential that depends analytically on the energy. In the present paper we are studying this transformation.