In this paper, we first study the Schrodinger operators with the following weighted function ___________, which is actually a finite linear combination of Dirac-Delta functions, and then discuss the same operator equipped with the same kind of potential function. With the aid of the boundary conditions, all possible eigenvalues and eigenfunctions of the self-adjoint Schrodinger operator are investigated. Furthermore, as a practical application, the spectrum distribution of such a Dirac-Delta type Schrodinger operator either weighted or potential is well applied to the remarkable integrable Camassa-Holm (CH) equation.
Fu, Shouzhong, Zhijun Qiao, and Zhong Wang. 2021. “Eigenvalues and Eigenfunctions of a Schr¨odinger Operator Associated with a Finite Combination of Dirac-Delta Functions and CH Peakons.” Journal of Nonlinear Modeling and Analysis 3 (1): 131–44. https://doi.org/10.12150/jnma.2021.131.
Journal of Nonlinear Modeling and Analysis