{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T07:56:02Z","timestamp":1769586962024,"version":"3.49.0"},"reference-count":56,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,3,21]],"date-time":"2021-03-21T00:00:00Z","timestamp":1616284800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper aims to explore nonlocal complex reverse-spacetime modified Korteweg-de Vries (mKdV) hierarchies via nonlocal symmetry reductions of matrix spectral problems and to construct their soliton solutions by the inverse scattering transforms. The corresponding inverse scattering problems are formulated by building the associated Riemann-Hilbert problems. A formulation of solutions to specific Riemann-Hilbert problems, with the jump matrix being the identity matrix, is established, where eigenvalues could equal adjoint eigenvalues, and thus N-soliton solutions to the nonlocal complex reverse-spacetime mKdV hierarchies are obtained from the reflectionless transforms.<\/jats:p>","DOI":"10.3390\/sym13030512","type":"journal-article","created":{"date-parts":[[2021,3,21]],"date-time":"2021-03-21T23:47:41Z","timestamp":1616370461000},"page":"512","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Inverse Scattering and Soliton Solutions of Nonlocal Complex Reverse-Spacetime Modified Korteweg-de Vries Hierarchies"],"prefix":"10.3390","volume":"13","author":[{"given":"Liming","family":"Ling","sequence":"first","affiliation":[{"name":"School of Mathematics, South China University of Technology, Guangzhou 510640, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5309-1493","authenticated-orcid":false,"given":"Wen-Xiu","family":"Ma","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China"},{"name":"Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia"},{"name":"Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA"},{"name":"School of Mathematical and Statistical Sciences, Mafikeng Campus, North-West University, Private Bag X2046, Mmabatho 2735, South Africa"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1111\/sapm.12153","article-title":"Integrable Nonlocal Nonlinear Equations","volume":"39","author":"Ablowitz","year":"2017","journal-title":"Stud. 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