Work

A hyper-block self-consistent approach to nonlinear Schrodinger equations: Breeding, metamorphosis, and killing of Hofstadter Butterflies

Year: 2021

Type: article

Abstract: Nonlinear Schrödinger equations play essential roles in different physics and engineering fields. In this paper, a hyper-block finite-difference self-consistent method (HFDSCF) is employed to solve this stationary nonlinear eigenvalue equation and demonstrated its accuracy. By comparing the results with the Sinc self-consistent (SSCF) method and exact available results, we show that the HFDSCF method gives quantum states with high accuracy and can even solve the strongly nonlinear Schrodinger equations. Then, by applying our method to Hofstadter butterfly problem, we describe the breeding, metamorphosis and killing of these butterflies by using nonlinear interactions as well as two constant length multi-well and sinusoidal potentials.

Source: Communications in Nonlinear Science and Numerical Simulation

DOI: 10.1016/j.cnsns.2021.105724

Authors: Mehdi Solaimani, S.M.A. Aleomraninejad

Institution: Qom University of Technology

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,130

OpenAlex ID: W3124716640

FWCI: 0.598

Cites: 34

Cited by: 3

Related to: 10