Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation |
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| Affiliation: | 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 |
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| 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. |
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| Keywords: | nonlinear Schrödinger equation soliton solutions asymptotic analysis soliton interactions |
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