Mathematics – Numerical Analysis
Scientific paper
2011-11-16
Mathematics
Numerical Analysis
19 pages, 20 fugures
Scientific paper
We consider the nonlinear Schr\"{o}dinger equation with a point-like source term. The soliton interaction with such a singular potential yields a critical solution behavior. That is, for the given value of the potential strength and the soliton amplitude, there exists a critical velocity of the initial soliton solution, around which the solution is either trapped by or transmitted through the potential. In this paper, we propose an efficient method for finding such a critical velocity by using the generalized polynomial chaos method. For the proposed method, we assume that the soliton velocity is a random variable and expand the solution in the random space using the orthogonal polynomials. The proposed method finds the critical velocity accurately with spectral convergence. Thus the computational complexity is much reduced. Numerical results for the smaller and higher values of the potential strength confirm the spectral convergence of the proposed method.
Chakraborty Debananda
Jung Jae-Hun
Lorin Emmanuel
No associations
LandOfFree
Efficient determination of critical parameters of nonlinear Schrödinger equation with point-like potential using generalized polynomial chaos methods does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Efficient determination of critical parameters of nonlinear Schrödinger equation with point-like potential using generalized polynomial chaos methods, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Efficient determination of critical parameters of nonlinear Schrödinger equation with point-like potential using generalized polynomial chaos methods will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-68872