Volume 21, Issue 1
A Compact Scheme for Coupled Stochastic Nonlinear Schrodinger Equations

Chuchu Chen, Jialin Hong, Lihai Ji & Linghua Kong

Commun. Comput. Phys., 21 (2017), pp. 93-125.

Published online: 2018-04

Preview Full PDF 395 853
Export citation
  • Abstract

In this paper, we propose a compact scheme to numerically study the coupled stochastic nonlinear Schr ¨odinger equations. We prove that the compact scheme preserves the discrete stochastic multi-symplectic conservation law, discrete charge conservation law and discrete energy evolution law almost surely. Numerical experiments confirm well the theoretical analysis results. Furthermore, we present a detailed numerical investigation of the optical phenomena based on the compact scheme. By numerical experiments for various amplitudes of noise, we find that the noise accelerates the oscillation of the soliton and leads to the decay of the solution amplitudes with respect to time. In particular, if the noise is relatively strong, the soliton will be totally destroyed. Meanwhile, we observe that the phase shift is sensibly modified by the noise. Moreover, the numerical results present inelastic interaction which is different from the deterministic case.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • References
  • Hide All
    View All

@Article{CiCP-21-93, author = {Chuchu Chen, Jialin Hong, Lihai Ji and Linghua Kong}, title = {A Compact Scheme for Coupled Stochastic Nonlinear Schrodinger Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {21}, number = {1}, pages = {93--125}, abstract = {

In this paper, we propose a compact scheme to numerically study the coupled stochastic nonlinear Schr ¨odinger equations. We prove that the compact scheme preserves the discrete stochastic multi-symplectic conservation law, discrete charge conservation law and discrete energy evolution law almost surely. Numerical experiments confirm well the theoretical analysis results. Furthermore, we present a detailed numerical investigation of the optical phenomena based on the compact scheme. By numerical experiments for various amplitudes of noise, we find that the noise accelerates the oscillation of the soliton and leads to the decay of the solution amplitudes with respect to time. In particular, if the noise is relatively strong, the soliton will be totally destroyed. Meanwhile, we observe that the phase shift is sensibly modified by the noise. Moreover, the numerical results present inelastic interaction which is different from the deterministic case.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.300815.180416a}, url = {http://global-sci.org/intro/article_detail/cicp/11233.html} }
Copy to clipboard
The citation has been copied to your clipboard