{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:25:05Z","timestamp":1787336705101,"version":"build-2736575974"},"reference-count":49,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"name":"Key R&D Program of China","award":["2020YFA0713400"],"award-info":[{"award-number":["2020YFA0713400"]}]},{"name":"Key R&D Program of China","award":["2020YFA0713401"],"award-info":[{"award-number":["2020YFA0713401"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171385"],"award-info":[{"award-number":["12171385"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971377"],"award-info":[{"award-number":["11971377"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007128","name":"Natural Science Foundation of Shaanxi Province","doi-asserted-by":"publisher","award":["2020JQ-008"],"award-info":[{"award-number":["2020JQ-008"]}],"id":[{"id":"10.13039\/501100007128","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,4,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>For the nonlinear conservative system, how to design an efficient scheme to preserve as manyinvariants as possible is a challenging task. The aim of this paper is to construct the finite difference\/spectral method for the Klein\u2013Gordon\u2013Schr\u00f6dinger (KGS) system on infinite domains [Formula: see text] ([Formula: see text], and 3) to conserve three kinds of the most important invariants, namely, the mass, the energy, and the momentum. Regarding the mass- and momentum-conservation laws as [Formula: see text] globally physical constraints, we elaborately combine the exponential scalar auxiliary variable (ESAV) approach and Lagrange multiplier approach to construct the ESAV\/Lagrange multiplier reformulation of the KGS system to preserve its original energy-conservation law. When solving the ESAV\/Lagrange multiplier reformulation, we employ the Hermite\u2013Galerkin spectral method for the spatial approximation and apply the Crank\u2013Nicolson scheme for the temporal discretization. At each time level, we only need to solve linearly algebraic systems with constant coefficients and a set of quadratic algebraic equations which can be efficiently solved by Newton iteration. We establish the conservation properties of the proposed method at the fullydiscrete level, which indicates that our scheme can preserve [Formula: see text] conserved quantities including mass, energy, and [Formula: see text] momentums of the KGS system. Numerical experiments are carried out to demonstrate the accuracy and conservation properties of the proposed scheme. As the applications of our scheme, we simulate the nonlinear interactions of vector solitons for KGS system in 2 dimensional\/3 dimensional cases.<\/jats:p>","DOI":"10.1137\/22m1484109","type":"journal-article","created":{"date-parts":[[2023,4,3]],"date-time":"2023-04-03T04:21:19Z","timestamp":1680495679000},"page":"B200-B230","source":"Crossref","is-referenced-by-count":15,"title":["Mass-, Energy-, and Momentum-Preserving Spectral Scheme for Klein-Gordon-Schr\u00f6dinger System on Infinite Domains"],"prefix":"10.1137","volume":"45","author":[{"given":"Shimin","family":"Guo","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liquan","family":"Mei","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenjing","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ying","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer Engineering and Science, Shanghai University, Shanghai 200444, China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,4,3]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/19M1264412"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2021.110328"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2007.02.018"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.38.619"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/0707049"},{"key":"ref6","doi-asserted-by":"crossref","first-page":"49","DOI":"10.3934\/dcds.2009.23.49","volume":"23","author":"Caffarelli L.","year":"2009","journal-title":"Discrete Contin. 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