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TME in optics allows for accurate manipulation of the spatial distribution of fluids or particles, resulting in improved light-matter interaction and the creation of new optofluidic devices for photonics, microscopy, and sensing applications. TME is same as the dynamic characteristics of soliton, appear in the Korteweg\u2013de Vries (KdV) equation. The KdV equation describes the evolution of weakly nonlinear, long waves in dispersive media. Through ansatz functions and logarithmic transformation in symbolic computation, we find some new exact solutions. We obtain Homoclinic breathers (HBs) with the usage of exponential and cosine ansatz. In addition, we obtain [Formula: see text]-shape rational solitons with the selection of quadratic ansatz. We also investigate two types of interactions involving [Formula: see text]-shaped solitons and kink waves. Through a combination of cosine, quadratic, and hyperbolic transformations, we achieve novel configurations and highly intriguing phenomena, namely, periodic cross-rational (PCR) and kink cross-rational (KCR) solitons. <\/jats:p>","DOI":"10.1142\/s1793962325500461","type":"journal-article","created":{"date-parts":[[2025,5,21]],"date-time":"2025-05-21T04:22:02Z","timestamp":1747801322000},"source":"Crossref","is-referenced-by-count":0,"title":["Study of thermophoretic motion equation used in optofluidic devices for nonlinear soliton waves"],"prefix":"10.1142","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7206-2508","authenticated-orcid":false,"given":"Syed T. 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