Malaysian Journal of Mathematical Sciences, February 2016, Vol. 10(S)
Special Issue: The 3rd International Conference on Mathematical Applications in Engineering 2014 (ICMAE'14)
Soliton Scattering on the External Potential in Weakly Nonlocal Nonlinear Media
Umarov, B. A. and Busul Aklan, N. A.
Corresponding Email: [email protected]
Received date: -
Accepted date: -
Abstract:
The Nonlinear Schr�dinger Equation (NLSE) is one of the universal mathematical models and it arises in a such diverse areas as plasma
physics, condensed matter physics, Bose - Einstein condensates, nonlinear optics, etc. In this work the scattering of the soliton of the generalized NLSE on the localized external potential has been studied, taking into account the weak nonlocality of the media. We have applied the approximate analytical method, namely the variational method to derive the equations for soliton parameters evolution during the scattering process. The validity of approximations were checked by direct numerical simulations with soliton initially located far from potential. It was shown that depending on initial velocity of the soliton, the soliton may be reflected by potential or transmitted through it. The critical values of the velocity separating these two scenarios have been identified.
Keywords: Soliton, nonlinear equations, scattering, variational methods
