{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:46:17Z","timestamp":1760147177092,"version":"build-2065373602"},"reference-count":71,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,16]],"date-time":"2023-01-16T00:00:00Z","timestamp":1673827200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["U2031145","11803020","11973020","41807437","12173071","2019JJD110006"],"award-info":[{"award-number":["U2031145","11803020","11973020","41807437","12173071","2019JJD110006"]}]},{"name":"Natural Science Foundation of Guangxi","award":["U2031145","11803020","11973020","41807437","12173071","2019JJD110006"],"award-info":[{"award-number":["U2031145","11803020","11973020","41807437","12173071","2019JJD110006"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The discovery of numerous close-in planets has updated our knowledge of planet formation. The tidal interaction between planets and host stars has a significant impact on the orbital and rotational evolution of the close planets. Tidal evolution usually takes a long time and requires reliable numerical methods. The manifold correction method, which strictly satisfies the integrals dissipative quasiintegrals of the system, exhibits good numerical accuracy and stability in the quasi-Kepler problem. Different manifold correction methods adopt different integrals or integral invariant relations to correct the numerical solutions. We apply the uncorrected five- and six-order Runge\u2013Kutta\u2013Fehlberg algorithm [RKF5(6)], as well as corrected by the velocity scaling method and Fukushima\u2019s linear transformation method to solve the tidal evolution of exoplanet systems. The results show that Fukushima\u2019s linear transformation method exhibits the best performance in the accuracy of the semimajor axis and eccentricity. In addition, we predict the tidal timescale of several current close exoplanetary systems by using this method.<\/jats:p>","DOI":"10.3390\/sym15010253","type":"journal-article","created":{"date-parts":[[2023,1,17]],"date-time":"2023-01-17T02:10:32Z","timestamp":1673921432000},"page":"253","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Application of Manifold Corrections in Tidal Evolution of Exoplanetary Systems"],"prefix":"10.3390","volume":"15","author":[{"given":"Qian-Qian","family":"Xiao","sequence":"first","affiliation":[{"name":"School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China"},{"name":"Center of Application and Research of Computational Physics, Shanghai University of Engineering Science, Shanghai 201620, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China"},{"name":"Center of Application and Research of Computational Physics, Shanghai University of Engineering Science, Shanghai 201620, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fu-Yao","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China"},{"name":"Center of Application and Research of Computational Physics, Shanghai University of Engineering Science, Shanghai 201620, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chen","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Astronomy and Space Science, Nanjing University, Nanjing 210023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China"},{"name":"Center of Application and Research of Computational Physics, Shanghai University of Engineering Science, Shanghai 201620, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1038\/378355a0","article-title":"A Jupiter-mass companion to a solar-type star","volume":"378","author":"Mayor","year":"1995","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1187","DOI":"10.1086\/177941","article-title":"Tidal decay close planetary orbits","volume":"470","author":"Rasio","year":"1996","journal-title":"Astrophys. 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