An explicit unconditionally stable numerical method for solving damped nonlinear Schrodinger equations with a focusing nonlinearity

Journal article

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. Ou...

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Authors: Bao, W; Jaksch, D

• Publication status: Published
• Journal: SIAM JOURNAL ON NUMERICAL ANALYSIS
• Volume: 41
• Issue: 4
• Pages: 1406-1426
• Publication date: 2003-01-01
• DOI: 10.1137/S0036142902413391
• EISSN: 1095-7170
• ISSN: 0036-1429
• Language: English
• Keywords: Bose-Einstein condensate (BEC); time-splitting sine-spectral (TSSP) method; complex Ginzburg-Landau (CGL); damped nonlinear Schrodinger equation (DNLS); Gross-Pitaevskii equation (GPE)