论文标题
椭圆形的有限频带的潜力
Elliptic finite-band potentials of a non-self-adjoint Dirac operator
论文作者
论文摘要
我们提供了一个有限带雅各比椭圆电位的显式两参数家族，该家族针对非夫妻dirac运算符，该家族连接了两个先前已知的限制案例，其中椭圆形参数为零或一个。通过将DIRAC操作员的周期性和反碘特征值问题与相应的特征值问题联系起来，用于在加权Hilbert空间中作用于傅立叶系数，并为HEUN方案适当的连接问题，可以使频谱的全面表征。反过来，这些问题与四个非自我配合的无界三角形运算符有关，尽管如此，所有这些都只有真实的特征值。对于某些参数值，相应的椭圆势会为聚焦非线性schrödinger层次结构的所有正和负流产生有限的溶液。
We present an explicit two-parameter family of finite-band Jacobi elliptic potentials for a non-self-adjoint Dirac operator which connects two previously known limiting cases in which the elliptic parameter is zero or one. A full characterization of the spectrum is obtained by relating the periodic and antiperiodic eigenvalue problems for the Dirac operator to corresponding eigenvalue problems for tridiagonal operators acting on Fourier coefficients in a weighted Hilbert space and to appropriate connection problems for Heun's equation. In turn, these problems are related to four non-self-adjoint unbounded tridiagonal operators, all of which nonetheless have only real eigenvalues. For certain parameter values, the corresponding elliptic potentials generate finite-genus solutions for all the positive and negative flows of the focusing nonlinear Schrödinger hierarchy.
