Eigenvalues and Eigenfunctions of a Schrödinger Operator Associated with a Finite Combination of Dirac-Delta Functions and CH Peakons
Year: 2021
Author: Shouzhong Fu, Zhijun Qiao, Zhong Wang
Journal of Nonlinear Modeling and Analysis, Vol. 3 (2021), Iss. 1 : pp. 131–144
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2021.131
Journal of Nonlinear Modeling and Analysis, Vol. 3 (2021), Iss. 1 : pp. 131–144
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Schrödinger operator Boundary conditions Soliton Peakon solution Cammassa-Holm equation.