TY - JOUR
T1 - Eigenvalues and Eigenfunctions of a Schrödinger Operator Associated with a Finite Combination of Dirac-Delta Functions and CH Peakons
AU - Fu , Shouzhong
AU - Qiao , Zhijun
AU - Wang , Zhong
JO - Journal of Nonlinear Modeling and Analysis
VL - 1
SP - 131
EP - 144
PY - 2021
DA - 2021/04
SN - 3
DO - http://doi.org/10.12150/jnma.2021.131
UR - https://global-sci.org/intro/article_detail/jnma/18782.html
KW - Schrödinger operator, Boundary conditions, Soliton, Peakon solution, Cammassa-Holm equation.
AB - <p style="text-align: justify;">In this paper, we first study the Schrödinger operators with the following weighted function $\sum\limits_{i=1}^n p_i \delta(x - a_i)$, 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 Schrödinger operator are investigated. Furthermore, as a practical application, the spectrum distribution of such a Dirac-Delta type Schrödinger operator either weighted or potential is well applied to the remarkable integrable Camassa-Holm (CH) equation.</p>