{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T08:36:01Z","timestamp":1768293361883,"version":"3.49.0"},"reference-count":63,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,3]],"date-time":"2025-06-03T00:00:00Z","timestamp":1748908800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The central objective of this study is to develop some different wave solutions and perform a qualitative analysis on the nonlinear dynamics of the time-fractional chiral nonlinear Schrodinger\u2019s equation (NLSE) in the conformable sense. Combined with the semi-inverse method (SIM) and traveling wave transformation, we establish the variational principle (VP). Based on this, the corresponding Hamiltonian is constructed. Adopting the Galilean transformation, the planar dynamical system is derived. Then, the phase portraits are plotted and the bifurcation analysis is presented to expound the existence conditions of the various wave solutions with the different shapes. Furthermore, the chaotic phenomenon is probed and sensitivity analysis is given in detail. Finally, two powerful tools, namely the variational method (VM) which stems from the VP and Ritz method, as well as the Hamiltonian-based method (HBM) that is based on the energy conservation theory, are adopted to find the abundant wave solutions, which are the bell-shape soliton (bright soliton), W-shape soliton (double-bright solitons or double bell-shaped soliton) and periodic wave solutions. The shapes of the attained new diverse wave solutions are simulated graphically, and the impact of the fractional order \u03b4 on the behaviors of the extracted wave solutions are also elaborated. To the authors\u2019 knowledge, the findings of this research have not been reported elsewhere and can enable us to gain a profound understanding of the dynamics characteristics of the investigative equation.<\/jats:p>","DOI":"10.3390\/axioms14060438","type":"journal-article","created":{"date-parts":[[2025,6,3]],"date-time":"2025-06-03T11:55:52Z","timestamp":1748951752000},"page":"438","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Dynamics of Abundant Wave Solutions to the Fractional Chiral Nonlinear Schrodinger\u2019s Equation: Phase Portraits, Variational Principle and Hamiltonian, Chaotic Behavior, Bifurcation and Sensitivity Analysis"],"prefix":"10.3390","volume":"14","author":[{"given":"Yu","family":"Tian","sequence":"first","affiliation":[{"name":"College of Physics and Telecommunication Engineering, Zhoukou Normal University, Zhoukou 466001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kang-Hua","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shao-Hui","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Physics and Telecommunication Engineering, Zhoukou Normal University, Zhoukou 466001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3905-0844","authenticated-orcid":false,"given":"Kang-Jia","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"125251","DOI":"10.1088\/1402-4896\/ac37a1","article-title":"An investigation of the physical dynamics of a traveling wave solution called a bright soliton","volume":"96","author":"Duran","year":"2021","journal-title":"Phys. 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