Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation

doi:10.1088/1674-1056/ac9822

中国物理B ›› 2023, Vol. 32 ›› Issue (1): 10505-010505.doi: 10.1088/1674-1056/ac9822

Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation

Xuefeng Zhang(张雪峰)^1,2, Tao Xu(许韬)^1,2,3,†, Min Li(李敏)⁴, and Yue Meng(孟悦)³

1 State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China;
2 College of Petroleum Engineering, China University of Petroleum, Beijing 102249, China;
3 College of Science, China University of Petroleum, Beijing 102249, China;
4 North China Electric Power University, Beijing 102206, China

收稿日期:2022-09-03 修回日期:2022-10-03 接受日期:2022-10-07 出版日期:2022-12-08 发布日期:2022-12-23
通讯作者: Tao Xu E-mail:xutao@cup.edu.cn
基金资助:
Project supported by the Natural Science Foundation of Beijing Municipality (Grant No. 1212007), the National Natural Science Foundation of China (Grant No. 11705284), and the Open Project Program of State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Grant No. PRP/DX-2211).

Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation

Xuefeng Zhang(张雪峰)^1,2, Tao Xu(许韬)^1,2,3,†, Min Li(李敏)⁴, and Yue Meng(孟悦)³

1 State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China;
2 College of Petroleum Engineering, China University of Petroleum, Beijing 102249, China;
3 College of Science, China University of Petroleum, Beijing 102249, China;
4 North China Electric Power University, Beijing 102206, China

Received:2022-09-03 Revised:2022-10-03 Accepted:2022-10-07 Online:2022-12-08 Published:2022-12-23
Contact: Tao Xu E-mail:xutao@cup.edu.cn
Supported by:
Project supported by the Natural Science Foundation of Beijing Municipality (Grant No. 1212007), the National Natural Science Foundation of China (Grant No. 11705284), and the Open Project Program of State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Grant No. PRP/DX-2211).

摘要/Abstract

摘要： We make a quantitative study on the soliton interactions in the nonlinear Schrödinger equation (NLSE) and its variable-coefficient (vc) counterpart. For the regular two-soliton and double-pole solutions of the NLSE, we employ the asymptotic analysis method to obtain the expressions of asymptotic solitons, and analyze the interaction properties based on the soliton physical quantities (especially the soliton accelerations and interaction forces); whereas for the bounded two-soliton solution, we numerically calculate the soliton center positions and accelerations, and discuss the soliton interaction scenarios in three typical bounded cases. Via some variable transformations, we also obtain the inhomogeneous regular two-soliton and double-pole solutions for the vcNLSE with an integrable condition. Based on the expressions of asymptotic solitons, we quantitatively study the two-soliton interactions with some inhomogeneous dispersion profiles, particularly discuss the influence of the variable dispersion function f(t) on the soliton interaction dynamics.

关键词: nonlinear Schrödinger equation, soliton solutions, asymptotic analysis, soliton interactions

Abstract: We make a quantitative study on the soliton interactions in the nonlinear Schrödinger equation (NLSE) and its variable-coefficient (vc) counterpart. For the regular two-soliton and double-pole solutions of the NLSE, we employ the asymptotic analysis method to obtain the expressions of asymptotic solitons, and analyze the interaction properties based on the soliton physical quantities (especially the soliton accelerations and interaction forces); whereas for the bounded two-soliton solution, we numerically calculate the soliton center positions and accelerations, and discuss the soliton interaction scenarios in three typical bounded cases. Via some variable transformations, we also obtain the inhomogeneous regular two-soliton and double-pole solutions for the vcNLSE with an integrable condition. Based on the expressions of asymptotic solitons, we quantitatively study the two-soliton interactions with some inhomogeneous dispersion profiles, particularly discuss the influence of the variable dispersion function f(t) on the soliton interaction dynamics.

Key words: nonlinear Schrödinger equation, soliton solutions, asymptotic analysis, soliton interactions

中图分类号: (Solitons)

05.45.Yv

02.30.Ik (Integrable systems) 42.65.Tg (Optical solitons; nonlinear guided waves)

Xuefeng Zhang(张雪峰), Tao Xu(许韬), Min Li(李敏), and Yue Meng(孟悦). Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation[J]. 中国物理B, 2023, 32(1): 10505-010505.

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Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation

Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation

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