Numerical methods and comparison for soliton solutions of the nonlinear Schrödinger equation

Jiayi Hu

doi:10.1117/12.2628213

22 April 2022 Numerical methods and comparison for soliton solutions of the nonlinear Schrödinger equation

Jiayi Hu

Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 121631Q (2022) https://doi.org/10.1117/12.2628213
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China

Abstract

The Schrödinger equation is a basic and key equation in quantum mechanics. In this thesis, we focus on the one-dimensional cubic-quintic nonlinear Schrödinger equation (CQNLSE). First, we introduce the general formulation of Schrödinger equation as well as some dynamic properties of the general nonlinear Schrödinger equation, including the mass and energy conservation. Second, we present four types of analytical solutions to the normalized CQNLSE and prove the conservation of energy of the CQNLSE. Third, we provide and analyze numerical methods, mainly finite difference methods and pseudo-spectral methods, for the CQNLSE under the zero far-field condition. Finally, we simulate the interaction of two bright solitons and dissect their condition and behavior before and after the collision.

Citation Download Citation

Jiayi Hu "Numerical methods and comparison for soliton solutions of the nonlinear Schrödinger equation", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 121631Q (22 April 2022); https://doi.org/10.1117/12.2628213

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available