{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T23:52:09Z","timestamp":1772236329086,"version":"3.50.1"},"reference-count":42,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,2]],"date-time":"2023-03-02T00:00:00Z","timestamp":1677715200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Prince Sattam Bin Abdulaziz University"},{"name":"Fahad Sameer Alshammari"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this study, we build multi-wave solutions of the KdV-5 model through Hirota\u2019s bilinear method. Taking complex conjugate values of the free parameters, various colliding exact solutions in the form of rogue wave, symmetric bell soliton and rogue waves form; breather waves, the interaction of a bell and rogue wave, and two colliding rogue wave solutions are constructed. To explore the characteristics of the breather waves, localized in any direction, the higher-order KdV-5 model, which describes the promulgation of weakly nonlinear elongated waves in a narrow channel, and ion-acoustic, and acoustic emission in harmonic crystals symmetrically is analyzed. With the appropriate parameters that affect and manage phase shifts, transmission routes, as well as energies of waves, a mixed solution relating to hyperbolic and sinusoidal expression are derived and illustrated by figures. All the single and multi-soliton appeared symmetric about an axis of the wave propagation. The analyzed outcomes are functional in achieving an understanding of the nonlinear situations in the mentioned fields.<\/jats:p>","DOI":"10.3390\/sym15030626","type":"journal-article","created":{"date-parts":[[2023,3,2]],"date-time":"2023-03-02T03:54:56Z","timestamp":1677729296000},"page":"626","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Dynamical Structures of Multi-Solitons and Interaction of Solitons to the Higher-Order KdV-5 Equation"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5402-8960","authenticated-orcid":false,"given":"Fahad Sameer","family":"Alshammari","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattambin Abdulaziz University, Alkharj 11942, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zillur","family":"Rahman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Comilla University, Cumilla 3506, Bangladesh"},{"name":"Department of Mathematics, Rajshahi University, Rajshahi 6205, Bangladesh"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1687-623X","authenticated-orcid":false,"given":"Harun-Or","family":"Roshid","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Pabna University of Science and Technology, Pabna 6600, Bangladesh"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad Safi","family":"Ullah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Comilla University, Cumilla 3506, Bangladesh"},{"name":"Department of Mathematics, Rajshahi University, Rajshahi 6205, Bangladesh"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdullah","family":"Aldurayhim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattambin Abdulaziz University, Alkharj 11942, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. Zulfikar","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Rajshahi University, Rajshahi 6205, Bangladesh"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"100017","DOI":"10.1016\/j.padiff.2020.100017","article-title":"Novel dynamics of wave solutions for Cahn-Allen and diffusive predator-prey models using MSE scheme","volume":"3","author":"Ullah","year":"2021","journal-title":"Partial. Differ. Equ. Appl. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1103\/RevModPhys.61.763","article-title":"Dynamics of solitons nearly integrable systems","volume":"61","author":"Kivshar","year":"1989","journal-title":"Rev. Mod. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Allahyani, S.A., Rehman, H.U., Awan, A.U., ElDin, E.M.T., and Hassan, M.U. (2022). 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