Chin. Phys. B, 2023, Vol. 32(1): 010505    DOI: 10.1088/1674-1056/ac9822
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# 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
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.
Keywords:  nonlinear Schrödinger equation      soliton solutions      asymptotic analysis      soliton interactions
Received:  03 September 2022      Revised:  03 October 2022      Accepted manuscript online:  07 October 2022
 PACS: 05.45.Yv (Solitons) 02.30.Ik (Integrable systems) 42.65.Tg (Optical solitons; nonlinear guided waves)
Fund: 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).
Corresponding Authors:  Tao Xu     E-mail:  xutao@cup.edu.cn