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We discuss two distinct nonlinear regimes: purely focusing cubic\u2013quintic media and inverted cubic\u2013quintic media\u2014featuring defocusing cubic and focusing quintic terms. Using the modified squared-operator method and Fourier collocation method, we analyze the existence domains, waveforms, powers and propagation constant relationships, and linear stability of fundamental solitons and their clusters. Our findings demonstrate that the combined action of saturable nonlinearities and nonlinear lattices effectively suppresses critical collapse and stabilizes diverse soliton structures, without relying on external linear periodic potentials or Bloch energy band theory. In both 1D and 2D systems, single solitons and their clusters tend to stabilize at larger propagation constants, with clusters exhibiting superior stability. Furthermore, the saturation coefficients S1 and S2 regulate the existence ranges, imposing strong saturation constraints on the propagation constants. In the competing (inverted) cubic\u2013quintic nonlinearities, stable solutions exist only when S2\u2009&amp;gt;\u2009S1. These results enrich the understanding of stable nonlinear localized modes in composite media with saturable nonlinearities and offer a theoretical framework for controlling optical localized modes in complex media, with potential applications in all-optical communication and information processing.<\/jats:p>","DOI":"10.1063\/5.0351143","type":"journal-article","created":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T13:24:21Z","timestamp":1792070661000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Solitons and their clusters sustained in saturable cubic\u2013quintic nonlinear lattices"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9603-5480","authenticated-orcid":false,"given":"Jiawei","family":"Li","sequence":"first","affiliation":[{"name":"School of Electronics and Communication Engineering, Guangzhou University 1 , Guangzhou 510006,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-4087-2991","authenticated-orcid":false,"given":"Yufan","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Electronics and Communication Engineering, Guangzhou University 1 , Guangzhou 510006,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2622-6425","authenticated-orcid":false,"given":"Milivoj R.","family":"Beli\u0107","sequence":"additional","affiliation":[{"name":"College of Science and Engineering, Hamad Bin Khalifa University 2 , 23874 Doha,","place":["Qatar"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6928-1064","authenticated-orcid":false,"given":"Jincheng","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Electronics and Information, Northwestern Polytechnical University 3 , Xi\u2019an 710072,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3218-8381","authenticated-orcid":false,"given":"Xing","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Arts and Sciences, Guangzhou Maritime University 4 , Guangzhou 510725,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9603-1845","authenticated-orcid":false,"given":"Liangwei","family":"Zeng","sequence":"additional","affiliation":[{"name":"School of Arts and Sciences, Guangzhou Maritime University 4 , Guangzhou 510725,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,10,15]]},"reference":[{"key":"2026101509241495700_c1","volume-title":"Optical Solitons: From Fibers to Photonic Crystals","year":"2003"},{"key":"2026101509241495700_c2","volume-title":"Physics of Solitons","year":"2006"},{"key":"2026101509241495700_c3","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1103\/RevModPhys.61.763","article-title":"Dynamics of solitons in nearly integrable systems","volume":"61","year":"1989","journal-title":"Rev. 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