{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,31]],"date-time":"2026-05-31T11:00:33Z","timestamp":1780225233871,"version":"3.54.0"},"reference-count":47,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Communications in Nonlinear Science and Numerical Simulation"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.cnsns.2026.110038","type":"journal-article","created":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T07:07:03Z","timestamp":1776323223000},"page":"110038","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"P1","title":["Quantifying chaos in nonlinear soliton solutions from the KFG equation and duffing oscillator"],"prefix":"10.1016","volume":"161","author":[{"given":"N.","family":"Cheemaa","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C.","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Abbas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"H.T.","family":"Nazish","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S.","family":"Saleem","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9394-4681","authenticated-orcid":false,"given":"A.","family":"Bekir","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"1","key":"10.1016\/j.cnsns.2026.110038_bib0001","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1515\/nleng-2014-0028","article-title":"Analytical solutions of linear and nonlinear Klein-Fock-Gordon equation","volume":"4","author":"Khan","year":"2015","journal-title":"Nonlinear Eng"},{"issue":"7","key":"10.1016\/j.cnsns.2026.110038_bib0002","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1016\/j.aml.2007.07.023","article-title":"The variational iteration method for studying the Klein\u2013Gordon equation","volume":"21","author":"Yusufo\u011flu","year":"2008","journal-title":"Appl Math Lett"},{"issue":"5","key":"10.1016\/j.cnsns.2026.110038_bib0003","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1016\/j.cpc.2008.11.012","article-title":"Differential transform method for solving the linear and nonlinear Klein\u2013Gordon equation","volume":"180","author":"Kanth","year":"2009","journal-title":"Comput Phys Commun"},{"issue":"6","key":"10.1016\/j.cnsns.2026.110038_bib0004","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/s10773-024-05692-x","article-title":"Exploration of soliton solutions in nonlinear optics for the third order Klein-Fock-Gordon equation and nonlinear Maccari\u2019s system","volume":"63","author":"Ahmad","year":"2024","journal-title":"Int J Theor Phys"},{"key":"10.1016\/j.cnsns.2026.110038_bib0005","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.rinp.2014.09.001","article-title":"Exact traveling wave solutions to the Klein\u2013Gordon equation using the novel (G\u2019\/G)-expansion method","volume":"4","author":"Hafez","year":"2014","journal-title":"Results Phys"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110038_bib0006","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1088\/0305-4470\/14\/2\/015","article-title":"Exact solution of the schrodinger and Klein-Gordon equations for generalised Hulthen potentials","volume":"14","author":"Znojil","year":"1981","journal-title":"J Phys A Math Gen"},{"issue":"4-5","key":"10.1016\/j.cnsns.2026.110038_bib0007","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/0375-9601(89)90555-0","article-title":"Bound states of the Klein-Gordon equation with vector and scalar Hulth\u2019en-type potentials","volume":"136","author":"Dominguez-Adame","year":"1989","journal-title":"Phys Lett A"},{"key":"10.1016\/j.cnsns.2026.110038_bib0008","series-title":"Exact bound state solutions of the s-wave Klein\u2013Gordon equation with the generalized Hulth\u00e9n potential","volume":"vol. 331","author":"Chen","year":"2004"},{"issue":"1-2","key":"10.1016\/j.cnsns.2026.110038_bib0009","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1016\/S0378-4371(96)00288-9","article-title":"Path integral for Klein-Gordon particle in vector plus scalar Hulth\u00e9n-type potentials","volume":"234","author":"Chetouani","year":"1996","journal-title":"Phys A"},{"issue":"4","key":"10.1016\/j.cnsns.2026.110038_bib0010","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/s10544-005-6070-2","article-title":"Characterization of polydimethylsiloxane (PDMS) properties for biomedical micro\/nanosystems","volume":"7","author":"Mata","year":"2005","journal-title":"Biomed Microdevices"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110038_bib0011","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1080\/17455030.2015.1099761","article-title":"New and more general traveling wave solutions for nonlinear schro\u00a8PLXdinger equation","volume":"26","author":"Cheemaa","year":"2016","journal-title":"Waves Random Complex Medium"},{"issue":"6","key":"10.1016\/j.cnsns.2026.110038_bib0012","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1088\/0253-6102\/65\/6\/671","article-title":"Dynamical behavior of solution in integrable nonlocal Lakshmanan\u2014Porsezian\u2014Daniel equation","volume":"65","author":"Liu","year":"2016","journal-title":"Commun Theor Phys"},{"key":"10.1016\/j.cnsns.2026.110038_bib0013","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.ijleo.2018.01.121","article-title":"Optical solitons to Lakshmanan-Porsezian-Daniel model for three nonlinear forms","volume":"160","author":"Jawad","year":"2018","journal-title":"Optik"},{"key":"10.1016\/j.cnsns.2026.110038_bib0014","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1016\/j.ijleo.2018.12.172","article-title":"Bright optical solitons for Lakshmanan\u2013Porsezian\u2013Daniel model with spatio-temporal dispersion by improved adomian decomposition method","volume":"181","author":"Al Qarni","year":"2019","journal-title":"Optik"},{"issue":"11","key":"10.1016\/j.cnsns.2026.110038_bib0015","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1140\/epjp\/i2017-11762-7","article-title":"Applications of the ETEM for obtaining optical soliton solutions for the Lakshmanan-Porsezian-Daniel model","volume":"132","author":"Manafian","year":"2017","journal-title":"Eur Phys J Plus"},{"key":"10.1016\/j.cnsns.2026.110038_bib0016","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1016\/j.ijleo.2017.12.190","article-title":"Optical solitons with Lakshmanan\u2013Porsezian\u2013Daniel model using a couple of integration schemes","volume":"158","author":"Biswas","year":"2018","journal-title":"Optik"},{"key":"10.1016\/j.cnsns.2026.110038_bib0017","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.ijleo.2018.02.091","article-title":"Optical solitons with Lakshmanan\u2013Porsezian\u2013Daniel model by modified extended direct algebraic method","volume":"162","author":"Hubert","year":"2018","journal-title":"Optik"},{"key":"10.1016\/j.cnsns.2026.110038_bib0018","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.ijleo.2017.06.102","article-title":"Optical solitons for Lakshmanan\u2013Porsezian\u2013Daniel model with spatio-temporal dispersion using the method of undetermined coefficients","volume":"144","author":"Vega-Guzman","year":"2017","journal-title":"Optik"},{"key":"10.1016\/j.cnsns.2026.110038_bib0019","doi-asserted-by":"crossref","first-page":"922","DOI":"10.1016\/j.ijleo.2019.01.057","article-title":"Optical solitons for Lakshmanan\u2013Porsezian\u2013Daniel model by Riccati equation approach","volume":"182","author":"AlQarni","year":"2019","journal-title":"Optik"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110038_bib0020","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1023\/A:1022852801087","article-title":"Theory of optical couplers","volume":"35","author":"Biswas","year":"2003","journal-title":"Opt Quantum Electron"},{"key":"10.1016\/j.cnsns.2026.110038_bib0021","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11082-016-0809-2","article-title":"On optical solitons: the chiral nonlinear schro\u00a8PLXdinger equation with perturbation and bohm potential","volume":"48","author":"Younis","year":"2016","journal-title":"Opt Quantum Electron"},{"issue":"31","key":"10.1016\/j.cnsns.2026.110038_bib0022","doi-asserted-by":"crossref","DOI":"10.1142\/S0217979220503014","article-title":"Chiral soliton solutions of perturbed chiral nonlinear Schr\u00f6dinger equation with its applications in mathematical physics","volume":"34","author":"Cheemaa","year":"2020","journal-title":"Int J Modern Phys B"},{"issue":"7","key":"10.1016\/j.cnsns.2026.110038_bib0023","doi-asserted-by":"crossref","first-page":"650","DOI":"10.1119\/1.17120","article-title":"Solitary wave solutions of nonlinear wave equations","volume":"60","author":"Malfliet","year":"1992","journal-title":"Am J Phys"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110038_bib0024","doi-asserted-by":"crossref","first-page":"1769","DOI":"10.1016\/j.apm.2015.08.018","article-title":"Modified extended tanh-function method and its applications to the Bogoyavlenskii equation","volume":"40","author":"Zahran","year":"2016","journal-title":"Appl Math Model"},{"issue":"4","key":"10.1016\/j.cnsns.2026.110038_bib0025","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1088\/0253-6102\/43\/4\/003","article-title":"Using symbolic computation to exactly solve the integrable Broer\u2013Kaupequations in (2+ 1)-dimensional spaces","volume":"43","author":"Fu-Ding","year":"2005","journal-title":"Commun Theor Phys"},{"issue":"22","key":"10.1016\/j.cnsns.2026.110038_bib0026","doi-asserted-by":"crossref","first-page":"10780","DOI":"10.1016\/j.ijleo.2016.08.115","article-title":"Auto-b\u00e4cklund transformation for some nonlinear partial differential equation","volume":"127","author":"Inan","year":"2016","journal-title":"Optik"},{"issue":"39","key":"10.1016\/j.cnsns.2026.110038_bib0027","doi-asserted-by":"crossref","first-page":"3459","DOI":"10.1016\/j.physleta.2011.07.058","article-title":"Painlev\u2019e analysis and symmetry group for the coupled Zakharov\u2013Kuznetsov equation","volume":"375","author":"Hu","year":"2011","journal-title":"Phys Lett A"},{"key":"10.1016\/j.cnsns.2026.110038_bib0028","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/j.cam.2017.03.011","article-title":"A modified numerical scheme and convergence analysis for fractional model of lienard\u2019s equation","volume":"339","author":"Kumar","year":"2018","journal-title":"J Comput Appl Math"},{"issue":"6","key":"10.1016\/j.cnsns.2026.110038_bib0029","doi-asserted-by":"crossref","first-page":"2248","DOI":"10.1016\/j.cnsns.2011.10.016","article-title":"One method for finding exact solutions of nonlinear differential equations","volume":"17","author":"Kudryashov","year":"2012","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110038_bib0030","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/j.cjph.2016.04.020","article-title":"Exponential rational function method for solving nonlinear equations arising in various physical models","volume":"54","author":"Bekir","year":"2016","journal-title":"Chin J Phys"},{"issue":"05","key":"10.1016\/j.cnsns.2026.110038_bib0031","doi-asserted-by":"crossref","DOI":"10.1142\/S0217984922502190","article-title":"A comparative study of nonlinear fractional Schr\u00f6dinger equation in optics","volume":"37","author":"Irshad","year":"2023","journal-title":"Mod Phys Lett B"},{"key":"10.1016\/j.cnsns.2026.110038_bib0032","doi-asserted-by":"crossref","first-page":"2325","DOI":"10.1016\/j.rinp.2017.06.049","article-title":"Elliptic and solitary wave solutions for Bogoyavlenskii equations system, couple Boiti-Leon-Pempinelli equations system and time-fractional Cahn-Allen equation","volume":"7","author":"Khater","year":"2017","journal-title":"Results Phys"},{"issue":"4","key":"10.1016\/j.cnsns.2026.110038_bib0033","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1016\/j.chaos.2005.10.048","article-title":"Auxiliary equation method and new solutions of Klein\u2013Gordon equations","volume":"31","author":"Sirendaoreji","year":"2007","journal-title":"Chaos Solitons Fractals"},{"key":"10.1016\/j.cnsns.2026.110038_bib0034","doi-asserted-by":"crossref","unstructured":"Cheemaa N., Seadawy A.R., Nazish H.T.. Dynamical nonlinear modified Korteweg\u2013De Vries equation arising in plasma physics and its analytical wave solutions2022a; 4:74\u201386.","DOI":"10.9734\/bpi\/ntpsr\/v4\/3667E"},{"key":"10.1016\/j.cnsns.2026.110038_bib0035","doi-asserted-by":"crossref","first-page":"31","DOI":"10.9734\/bpi\/ntpsr\/v1\/1969B","article-title":"Bright\u2013dark solitary wave solutions of coupled integrable (2+ 1)-dimensional maccari system in applied physics","volume":"1","author":"Cheemaa","year":"2022","journal-title":"New Trends Phys Sci Res"},{"key":"10.1016\/j.cnsns.2026.110038_bib0036","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2022.112975","article-title":"Dynamics exploration for a fractional-order delayed Zooplankton\u2013Phytoplankton system","volume":"166","author":"Li","year":"2023","journal-title":"Chaos Solitons Fractals"},{"key":"10.1016\/j.cnsns.2026.110038_bib0037","first-page":"2906","article-title":"Bifurcations of twisted fine heteroclinic loop for high-dimensional systems","volume":"13","author":"Jin","year":"2023","journal-title":"J Appl Anal Comput"},{"key":"10.1016\/j.cnsns.2026.110038_bib0038","doi-asserted-by":"crossref","DOI":"10.1142\/S0218127422500596","article-title":"Chaos induced by heteroclinic cycles connecting repellers for first-order partial difference equations","volume":"32","author":"Li","year":"2022","journal-title":"Int J Bifurcation Chaos"},{"issue":"2","key":"10.1016\/j.cnsns.2026.110038_bib0039","first-page":"1035","article-title":"Hunting cooperation and gestation delay in a prey\u2013predator model with fractional derivative","volume":"16","author":"Xu","year":"2026","journal-title":"J Appl Anal Comput"},{"issue":"3","key":"10.1016\/j.cnsns.2026.110038_bib0040","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1007\/s11082-023-05985-1","article-title":"Nonlinear fiber optics with water wave flumes: dynamics of the optical solitons of the derivative nonlinear schro\u00a8PLXdinger equation","volume":"56","author":"Pan","year":"2024","journal-title":"Opt Quantum Electron"},{"issue":"9","key":"10.1016\/j.cnsns.2026.110038_bib0041","doi-asserted-by":"crossref","first-page":"1127","DOI":"10.1515\/IJNSNS.2009.10.9.1127","article-title":"Analytical study of Navier-Stokes equation with fractional orders using he\u2019s homotopy perturbation and variational iteration methods","volume":"10","author":"Khan","year":"2009","journal-title":"Int J Nonlinear Sci Numer Simul"},{"key":"10.1016\/j.cnsns.2026.110038_bib0042","series-title":"Soliton Solutions of Klein\u2013Fock\u2013Gordon Equation Using Sardar Subequation Method","volume":"vol. 10","author":"Rehman","year":"2022"},{"issue":"12","key":"10.1016\/j.cnsns.2026.110038_bib0043","doi-asserted-by":"crossref","DOI":"10.1007\/s11182-021-02283-9","article-title":"Analytical solution of the Klein\u2013Fock\u2013Gordon equation for the Rosen\u2013Morse potential","volume":"63","author":"Aliyeva","year":"2021","journal-title":"Russ Phys J"},{"key":"10.1016\/j.cnsns.2026.110038_bib0044","series-title":"Investigating the Impact of Fractional Non-Linearity in the Klein\u2013Fock\u2013Gordon Equation on Quantum Dynamics","volume":"vol. 15","author":"Noor","year":"2023"},{"issue":"33","key":"10.1016\/j.cnsns.2026.110038_bib0045","doi-asserted-by":"crossref","DOI":"10.1142\/S0217751X18502032","article-title":"Bound state solution of the Klein\u2013Fock\u2013Gordon equation with the Hulth\u00e9n plus a ring-shaped-like potential within SUSY quantum mechanics","volume":"33","author":"Ahmadov","year":"2018","journal-title":"Int J Modern Phys A"},{"issue":"1","key":"10.1016\/j.cnsns.2026.110038_bib0046","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1515\/nleng-2014-0028","article-title":"Analytical solutions of linear and nonlinear Klein-Fock-Gordon equation","volume":"4","author":"Khan","year":"2015","journal-title":"Nonlinear Eng"},{"key":"10.1016\/j.cnsns.2026.110038_bib0047","article-title":"Chaotic dynamics of non-autonomous nonlinear system for a sandwich plate with truss core","volume":"10","year":"2022","journal-title":"Mathematics"}],"container-title":["Communications in Nonlinear Science and Numerical Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426003977?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426003977?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,31]],"date-time":"2026-05-31T10:03:21Z","timestamp":1780221801000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1007570426003977"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":47,"alternative-id":["S1007570426003977"],"URL":"https:\/\/doi.org\/10.1016\/j.cnsns.2026.110038","relation":{},"ISSN":["1007-5704"],"issn-type":[{"value":"1007-5704","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Quantifying chaos in nonlinear soliton solutions from the KFG equation and duffing oscillator","name":"articletitle","label":"Article Title"},{"value":"Communications in Nonlinear Science and Numerical Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cnsns.2026.110038","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"110038"}}