{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T13:37:42Z","timestamp":1762349862152,"version":"build-2065373602"},"reference-count":39,"publisher":"Walter de Gruyter GmbH","issue":"4","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11801277"],"award-info":[{"award-number":["11801277"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    This paper aims to give a unified construction framework of meshless structure-preserving algorithms to solve the\n                    <jats:italic>d<\/jats:italic>\n                    -dimensional (\n                    <jats:inline-formula id=\"j_cmam-2023-0213_ineq_9999\">\n                      <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <m:mrow>\n                            <m:mi>d<\/m:mi>\n                            <m:mo>=<\/m:mo>\n                            <m:mn>1<\/m:mn>\n                          <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2023-0213_eq_0241.png\"\/>\n                        <jats:tex-math>{d=1}<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    or 2) nonlinear Schr\u00f6dinger equation. Based on the method of lines, we first derive a finite-dimensional Hamiltonian system by using the radial basis function method of the quasi-interpolation and the technique of left-multiplying a diagonal matrix to discretize the space direction. Then suitable geometric numerical integrations can be used to discretize the time direction, which yields a class of meshless structure-preserving algorithms. In addition to the construction, the structure-preserving properties and their proofs are also provided in detail. Besides the uniform and nonuniform grids, the numerical experiments on the random grids are also emphasized to verify the theoretical research well, which is of great significance for scattering points based on the characteristics of actual problems.\n                  <\/jats:p>","DOI":"10.1515\/cmam-2023-0213","type":"journal-article","created":{"date-parts":[[2024,11,14]],"date-time":"2024-11-14T07:25:45Z","timestamp":1731569145000},"page":"1003-1016","source":"Crossref","is-referenced-by-count":0,"title":["A Class of Meshless Structure-Preserving Algorithms for the Nonlinear Schr\u00f6dinger Equation"],"prefix":"10.1515","volume":"25","author":[{"given":"Jialing","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics , 71127 Nanjing University of Information Science and Technology , Nanjing 210044 , P. R. China"}]},{"given":"Zhengting","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics , 71127 Nanjing University of Information Science and Technology , Nanjing 210044 , P. R. China"}]},{"given":"Zhoujin","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics , 71127 Nanjing University of Information Science and Technology , Nanjing 210044 , P. R. China"}]}],"member":"374","published-online":{"date-parts":[[2024,11,14]]},"reference":[{"key":"2025110513331148266_j_cmam-2023-0213_ref_001","doi-asserted-by":"crossref","unstructured":"S.  Abbasbandy, H.  Roohani Ghehsareh and I.  Hashim,\nA meshfree method for the solution of two-dimensional cubic nonlinear Schr\u00f6dinger equation,\nEng. Anal. Bound. Elem. 37 (2013), no. 6, 885\u2013898.","DOI":"10.1016\/j.enganabound.2013.03.006"},{"key":"2025110513331148266_j_cmam-2023-0213_ref_002","doi-asserted-by":"crossref","unstructured":"W.  Bao and Y.  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