An explicit unconditionally stable numerical method for solving damped nonlinear Schrodinger equations with a focusing nonlinearity
This paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schrödinger equations (NLSs). The method is explicit, unconditionally stable, and time transversal invariant. Moreover, it preserves the exact decay rate for the normalization o...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
2003
|
| _version_ | 1797052798705074176 |
|---|---|
| author | Bao, W Jaksch, D |
| author_facet | Bao, W Jaksch, D |
| author_sort | Bao, W |
| collection | OXFORD |
| description | This paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schrödinger equations (NLSs). The method is explicit, unconditionally stable, and time transversal invariant. Moreover, it preserves the exact decay rate for the normalization of the wave function if linear damping terms are added to the NLS. Extensive numerical tests are presented for cubic focusing NLSs in two dimensions with a linear, cubic, or quintic damping term. Our numerical results show that quintic or cubic damping always arrests blowup, while linear damping can arrest blowup only when the damping parameter δ is larger than a threshold value δ th. We note that our method can also be applied to solve the three-dimensional Gross-Pitaevskii equation with a quintic damping term to model the dynamics of a collapsing and exploding Bose-Einstein condensate (BEC). |
| first_indexed | 2024-03-06T18:35:44Z |
| format | Journal article |
| id | oxford-uuid:0b289cca-4429-4415-830f-c06e1d2c789a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:35:44Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | oxford-uuid:0b289cca-4429-4415-830f-c06e1d2c789a2022-03-26T09:27:55ZAn explicit unconditionally stable numerical method for solving damped nonlinear Schrodinger equations with a focusing nonlinearityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0b289cca-4429-4415-830f-c06e1d2c789aEnglishSymplectic Elements at Oxford2003Bao, WJaksch, DThis paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schrödinger equations (NLSs). The method is explicit, unconditionally stable, and time transversal invariant. Moreover, it preserves the exact decay rate for the normalization of the wave function if linear damping terms are added to the NLS. Extensive numerical tests are presented for cubic focusing NLSs in two dimensions with a linear, cubic, or quintic damping term. Our numerical results show that quintic or cubic damping always arrests blowup, while linear damping can arrest blowup only when the damping parameter δ is larger than a threshold value δ th. We note that our method can also be applied to solve the three-dimensional Gross-Pitaevskii equation with a quintic damping term to model the dynamics of a collapsing and exploding Bose-Einstein condensate (BEC). |
| spellingShingle | Bao, W Jaksch, D An explicit unconditionally stable numerical method for solving damped nonlinear Schrodinger equations with a focusing nonlinearity |
| title | An explicit unconditionally stable numerical method for solving damped nonlinear Schrodinger equations with a focusing nonlinearity |
| title_full | An explicit unconditionally stable numerical method for solving damped nonlinear Schrodinger equations with a focusing nonlinearity |
| title_fullStr | An explicit unconditionally stable numerical method for solving damped nonlinear Schrodinger equations with a focusing nonlinearity |
| title_full_unstemmed | An explicit unconditionally stable numerical method for solving damped nonlinear Schrodinger equations with a focusing nonlinearity |
| title_short | An explicit unconditionally stable numerical method for solving damped nonlinear Schrodinger equations with a focusing nonlinearity |
| title_sort | explicit unconditionally stable numerical method for solving damped nonlinear schrodinger equations with a focusing nonlinearity |
| work_keys_str_mv | AT baow anexplicitunconditionallystablenumericalmethodforsolvingdampednonlinearschrodingerequationswithafocusingnonlinearity AT jakschd anexplicitunconditionallystablenumericalmethodforsolvingdampednonlinearschrodingerequationswithafocusingnonlinearity AT baow explicitunconditionallystablenumericalmethodforsolvingdampednonlinearschrodingerequationswithafocusingnonlinearity AT jakschd explicitunconditionallystablenumericalmethodforsolvingdampednonlinearschrodingerequationswithafocusingnonlinearity |