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Appl. Dyn. Syst."],"published-print":{"date-parts":[[2024,3,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>This paper studies the soliton dynamics for the Rabi-coupled Gross\u2013Pitaevskii model in multicomponent Bose\u2013Einstein condensates. The model has variable nonlinearities and external potentials and is used to construct a complex multisoliton in an explicit form. The variable nonlinearity and external potential cause the soliton to compress and change its velocity, respectively. A new generalized similarity transformation is proposed to eliminate the [Formula: see text] Rabi-coupled terms in the [Formula: see text]-component model, which can make the Hirota bilinear method be applied to obtain multisoliton solutions. The bound state of the two-soliton forms the soliton molecule under velocity resonance. Asymptotic analysis can give the asymptotic expressions of each single soliton in multisoliton solutions, which can clearly give each soliton\u2019s width, velocity, amplitude, and energy; these parameters can control multisolitons. When the solitons\u2019 relative velocity or the solitons\u2019 width is large, the interferogram between solitons will be observed. Numerical simulation shows that these solitons can steadily propagate. It is easy for the soliton molecule and interference dynamics to occur because of the controlled soliton. Since the coupled Gross\u2013Pitaevskii equation describes the mechanics of matter waves in Bose\u2013Einstein condensates, it is proved that we can observe the stable solitons and soliton molecules in Bose\u2013Einstein condensates. The method and results presented in this paper are also common to other similar models. When observing particle multiple distributions, quantum interferometry, and interferometers, the results presented and the model in this paper can provide a reference for these applications.<\/jats:p>","DOI":"10.1137\/23m155551x","type":"journal-article","created":{"date-parts":[[2024,2,28]],"date-time":"2024-02-28T03:11:16Z","timestamp":1709089876000},"page":"748-778","source":"Crossref","is-referenced-by-count":20,"title":["Dynamics of Controllable Matter-Wave Solitons and Soliton Molecules for a Rabi-Coupled Gross\u2013Pitaevskii Equation with Temporally and Spatially Modulated Coefficients"],"prefix":"10.1137","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0816-6211","authenticated-orcid":true,"given":"Haotian","family":"Wang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Information Photonics and Optical Communications, School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing 100876, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hujiang","family":"Yang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Photonics and Optical Communications, School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing 100876, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiankui","family":"Meng","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Photonics and Optical Communications, School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing 100876, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ye","family":"Tian","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Photonics and Optical Communications, School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing 100876, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenjun","family":"Liu","sequence":"additional","affiliation":[{"name":"Corresponding author. State Key Laboratory of Information Photonics and Optical Communications, School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing 100876, People\u2019s Republic of China, and Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University, Baoding 071000, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,2,28]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1126\/science.269.5221.198"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.75.3969"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.75.1687"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1126\/science.1071021"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.83.5198"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2007.02.067"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1137\/090775324"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1038\/nphys1177"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.83.2498"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1137\/140992345"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.84.053607"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.89.100403"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.71.036625"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.80.023617"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.72.023611"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1038\/415039a"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.91.240405"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.96.170401"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1038\/nature747"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1126\/science.287.5450.97"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-73591-5"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2022.128283"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2017.11.035"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.95.053618"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.80.033610"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2021.105983"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-021-06851-z"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.125.183902"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.67.033601"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.67.013608"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1038\/45194"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1126\/science.283.5408.1706"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.129.073902"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2022.128284"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.48.3186"},{"key":"ref36","volume-title":"Quantum Optics","author":"Scully M. 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