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Kosloff and D. Kosloff,\nAbsorbing boundaries for wave propagation problems,\nJ. Comput. Phys. 63 1986, 2, 363\u2013376].\nWe also show that our imaginary potential function\nis more efficient than what is used in the literature.\nNumerical examples show that our ansatz is significantly better than existing approaches.\nWe show that our approach can very accurately compute the solutions of\nthe NLS equations in one dimension,\nincluding in the case of multi-dominant wave number solutions.<\/jats:p>","DOI":"10.1515\/cmam-2023-0096","type":"journal-article","created":{"date-parts":[[2023,10,31]],"date-time":"2023-10-31T10:51:07Z","timestamp":1698749467000},"page":"797-812","source":"Crossref","is-referenced-by-count":1,"title":["Adaptive Absorbing Boundary Layer for the Nonlinear Schr\u00f6dinger Equation"],"prefix":"10.1515","volume":"24","author":[{"given":"Hans Peter","family":"Stimming","sequence":"first","affiliation":[{"name":"Research platform MMM, c\/o Fakult\u00e4t f\u00fcr Mathematik , Universit\u00e4t Wien , Oskar-Morgenstern-Platz 1, A-1090 Vienna , Austria"}]},{"given":"Xin","family":"Wen","sequence":"additional","affiliation":[{"name":"Institute of Computational Mathematics , Academy of Mathematics and Systems Science , Chinese Academy of Sciences , P.\u2009O. Box 2719 , Beijing 100080 , P. R. China"}]},{"given":"Norbert J.","family":"Mauser","sequence":"additional","affiliation":[{"name":"Research platform MMM, c\/o Fakult\u00e4t f\u00fcr Mathematik , Universit\u00e4t Wien , Oskar-Morgenstern-Platz 1, A-1090 Vienna , Austria"}]}],"member":"374","published-online":{"date-parts":[[2023,11,1]]},"reference":[{"key":"2024070116104869602_j_cmam-2023-0096_ref_001","doi-asserted-by":"crossref","unstructured":"I.  Alonso-Mallo and N.  Reguera,\nWeak ill-posedness of spatial discretizations of absorbing boundary conditions for Schr\u00f6dinger-type equations,\nSIAM J. Numer. Anal. 40 (2002), no. 1, 134\u2013158.","DOI":"10.1137\/S0036142900374433"},{"key":"2024070116104869602_j_cmam-2023-0096_ref_002","doi-asserted-by":"crossref","unstructured":"I.  Alonso-Mallo and N.  Reguera,\nDiscrete absorbing boundary conditions for Schr\u00f6dinger-type equations, construction and error analysis,\nSIAM J. Numer. 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Phys. 188 (2003), no. 1, 157\u2013175.","DOI":"10.1016\/S0021-9991(03)00159-1"},{"key":"2024070116104869602_j_cmam-2023-0096_ref_005","doi-asserted-by":"crossref","unstructured":"X.  Antoine, C.  Besse and S.  Descombes,\nArtificial boundary conditions for one-dimensional cubic nonlinear Schr\u00f6dinger equations,\nSIAM J. Numer. Anal. 43 (2006), no. 6, 2272\u20132293.","DOI":"10.1137\/040606983"},{"key":"2024070116104869602_j_cmam-2023-0096_ref_006","doi-asserted-by":"crossref","unstructured":"X.  Antoine, C.  Besse and P.  Klein,\nAbsorbing boundary conditions for general nonlinear Schr\u00f6dinger equations,\nSIAM J. Sci. Comput. 33 (2011), no. 2, 1008\u20131033.","DOI":"10.1137\/090780535"},{"key":"2024070116104869602_j_cmam-2023-0096_ref_007","doi-asserted-by":"crossref","unstructured":"X.  Antoine, C.  Besse and P.  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