Isospectral Flows of Third Order Operators
Isospectral Flows of Third Order Operators
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DOI：
10.1137/s0036141098347249
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
L. Amour
中科院分区：
文献类型：
--
作者：
L. Amour
We consider the third order linear differential operator $L_{p,q}=i\frac{d^3}{dx^3}+i\frac{d}{dx}q+iq\frac{d}{dx}+p$ on the unit interval. The associated boundary conditions are $y(0)=y(1)=0$, $y'(0)=zy'(1)$ with $z\in\C,\ \vert z\vert=1$. For all but a finite number of parameters z, the eigenvalues $\lambda_{j}$ of $L_{p,q}$ are of multiplicity one. For fixed boundary conditions we make the formulae for isospectral flows induced by the Hamiltonian function $\lambda_{j}$ explicit. These flows commute.
We consider the third order linear differential operator $L_{p,q}=i\frac{d^3}{dx^3}+i\frac{d}{dx}q+iq\frac{d}{dx}+p$ on the unit interval. The associated boundary conditions are $y(0)=y(1)=0$, $y'(0)=zy'(1)$ with $z\in\C,\ \vert z\vert=1$. For all but a finite number of parameters z, the eigenvalues $\lambda_{j}$ of $L_{p,q}$ are of multiplicity one. For fixed boundary conditions we make the formulae for isospectral flows induced by the Hamiltonian function $\lambda_{j}$ explicit. These flows commute.