Eigenvalues and Eigenfunctions of a Schrödinger Operator Associated with a Finite Combination of Dirac-Delta Functions and CH Peakons

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.

Author Details

Shouzhong Fu

Zhijun Qiao

Zhong Wang