{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T13:57:57Z","timestamp":1772978277065,"version":"3.50.1"},"reference-count":54,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12461031"],"award-info":[{"award-number":["12461031"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12301215"],"award-info":[{"award-number":["12301215"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100017700","name":"Henan Provincial Science and Technology Research Project","doi-asserted-by":"publisher","award":["252102220057"],"award-info":[{"award-number":["252102220057"]}],"id":[{"id":"10.13039\/501100017700","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004607","name":"Guangxi Natural Science Foundation","doi-asserted-by":"publisher","award":["2024GXNSFBA010384"],"award-info":[{"award-number":["2024GXNSFBA010384"]}],"id":[{"id":"10.13039\/501100004607","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Zhejiang Province Natural Science Foundation","doi-asserted-by":"publisher","award":["LQ23A010009"],"award-info":[{"award-number":["LQ23A010009"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Communications in Nonlinear Science and Numerical Simulation"],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1016\/j.cnsns.2026.109876","type":"journal-article","created":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T07:42:59Z","timestamp":1772178179000},"page":"109876","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Periodic and solitary waves in a generalized delayed KP-MEW equation with arbitrarily high-order nonlinearity"],"prefix":"10.1016","volume":"159","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8772-4794","authenticated-orcid":false,"given":"Yanfei","family":"Dai","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0007-0140-230X","authenticated-orcid":false,"given":"Tianrui","family":"An","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0972-047X","authenticated-orcid":false,"given":"Minzhi","family":"Wei","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5703-2180","authenticated-orcid":false,"given":"Huiyang","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"5","key":"10.1016\/j.cnsns.2026.109876_bib0001","first-page":"422","article-title":"On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves","volume":"39","author":"Korteweg","year":"1895","journal-title":"Phil Magaz"},{"key":"10.1016\/j.cnsns.2026.109876_bib0002","series-title":"Nonlinear evolution equations and inverse scattering","author":"Ablowitz","year":"1991"},{"key":"10.1016\/j.cnsns.2026.109876_bib0003","first-page":"389","article-title":"A mathematical justification for Korteweg-de Vries equation and Boussinesq equation of water surface waves","volume":"23","author":"Kano","year":"1986","journal-title":"Osaka J Math"},{"key":"10.1016\/j.cnsns.2026.109876_bib0004","doi-asserted-by":"crossref","first-page":"1108","DOI":"10.1103\/PhysRevLett.25.1108","article-title":"Asymptotic theory of self-trapping of heat pulses in solids","volume":"25","author":"Tappert","year":"1970","journal-title":"Phys Rev Lett"},{"key":"10.1016\/j.cnsns.2026.109876_bib0005","first-page":"285","article-title":"On the stability of the KP equation and application to shallow water waves","volume":"39","author":"Kadomtsev","year":"1974","journal-title":"Sov Phys JETP"},{"key":"10.1016\/j.cnsns.2026.109876_bib0006","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1111\/j.1467-9590.2009.00448.x","article-title":"Soliton solutions of the KP equation and application to shallow water wave","volume":"123","author":"Chakravarty","year":"2009","journal-title":"Stud Appl Math"},{"key":"10.1016\/j.cnsns.2026.109876_bib0007","series-title":"Darboux transformations and solitons","author":"Matveev","year":"1991"},{"key":"10.1016\/j.cnsns.2026.109876_bib0008","series-title":"The direct method in soliton theory","author":"Hirota","year":"2004"},{"issue":"8","key":"10.1016\/j.cnsns.2026.109876_bib0009","doi-asserted-by":"crossref","first-page":"1538","DOI":"10.1016\/j.cnsns.2006.09.018","article-title":"Solitary wave solutions of the modified equal width wave equation","volume":"13","author":"Esen","year":"2008","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"10.1016\/j.cnsns.2026.109876_bib0010","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/S0010-4655(99)00471-3","article-title":"Solitary wave interactions for the modified equal width equation","volume":"126","author":"Zaki","year":"2000","journal-title":"Comput Phys Commun"},{"key":"10.1016\/j.cnsns.2026.109876_bib0011","doi-asserted-by":"crossref","first-page":"1879","DOI":"10.1016\/j.camwa.2017.02.017","article-title":"Dynamics of the generalized KP-MEW-burgers equation with external periodic perturbation","volume":"73","author":"Saha","year":"2017","journal-title":"Comput Math Appl"},{"issue":"2","key":"10.1016\/j.cnsns.2026.109876_bib0012","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1080\/00207160412331296706","article-title":"The tanh method and the sine-cosine method for solving the KP-MEW equation","volume":"82","author":"Wazwaz","year":"2005","journal-title":"Int J Comput Math"},{"key":"10.1016\/j.cnsns.2026.109876_bib0013","doi-asserted-by":"crossref","first-page":"3539","DOI":"10.1016\/j.cnsns.2012.01.005","article-title":"Bifurcation of travelling wave solutions for the generalized KP-MEW equations","volume":"17","author":"Saha","year":"2012","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"10.1016\/j.cnsns.2026.109876_bib0014","first-page":"8979","article-title":"Single peak solitary wave solutions for the generalized KP-MEW (2, 2) equation under boundary condition","volume":"219","author":"Wei","year":"2013","journal-title":"Appl Math Comput"},{"key":"10.1016\/j.cnsns.2026.109876_bib0015","doi-asserted-by":"crossref","first-page":"1775","DOI":"10.1016\/j.camwa.2014.10.013","article-title":"Compacton, peakon, cuspons, loop solutions and smooth solitons for the generalized KP-MEW equation","volume":"68","author":"Zhong","year":"2014","journal-title":"Comput Math Appl"},{"key":"10.1016\/j.cnsns.2026.109876_bib0016","doi-asserted-by":"crossref","first-page":"3620","DOI":"10.1016\/j.camwa.2019.06.013","article-title":"Applications of propagation of long-wave with dissipation and dispersion in nonlinear media via solitary wave solutions of generalized Kadomtsev-Petviashvili modified equal width dynamical equation","volume":"78","author":"Seadawy","year":"2019","journal-title":"Comput Math Appl"},{"key":"10.1016\/j.cnsns.2026.109876_bib0017","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/j.joes.2021.08.013","article-title":"On the modified (g\u2032\/g2)-expansion method for finding some analytical solutions of the traveling waves","volume":"7","author":"Behera","year":"2022","journal-title":"J Ocean Eng Sci"},{"issue":"3","key":"10.1016\/j.cnsns.2026.109876_bib0018","doi-asserted-by":"crossref","DOI":"10.1088\/0031-8949\/89\/03\/035202","article-title":"Compacton-like wave and kink-like wave solutions of the generalized KP-MEW (2, 2) equation","volume":"89","author":"Li","year":"2014","journal-title":"Phys Scripta"},{"issue":"1","key":"10.1016\/j.cnsns.2026.109876_bib0019","article-title":"Some smooth and nonsmooth traveling wave solutions for KP-MEW (2, 2) equation","volume":"2021","author":"He","year":"2021","journal-title":"J Math"},{"key":"10.1016\/j.cnsns.2026.109876_bib0020","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1007\/BF03167282","article-title":"On the uniqueness of traveling waves in perturbed Korteweg-de Vries equations","volume":"10","author":"Derks","year":"1993","journal-title":"Jpn J Indust Appl Math"},{"key":"10.1016\/j.cnsns.2026.109876_bib0021","doi-asserted-by":"crossref","first-page":"401","DOI":"10.32917\/hmj\/1206128032","article-title":"Travelling wave solutions to a perturbed Korteweg-de Vries equation","volume":"24","author":"Ogawa","year":"1994","journal-title":"Hiroshima Math J"},{"key":"10.1016\/j.cnsns.2026.109876_bib0022","doi-asserted-by":"crossref","first-page":"537","DOI":"10.3846\/13926292.2014.960016","article-title":"Existence of solitary waves and periodic waves to a perturbed generalized KdV equation","volume":"19","author":"Yan","year":"2014","journal-title":"Math Mod Anal"},{"key":"10.1016\/j.cnsns.2026.109876_bib0023","doi-asserted-by":"crossref","first-page":"5324","DOI":"10.1016\/j.jde.2016.08.003","article-title":"Existence of solitary waves and periodic waves for a perturbed generalized BBM equation","volume":"261","author":"Chen","year":"2016","journal-title":"J Differ Equ"},{"key":"10.1016\/j.cnsns.2026.109876_bib0024","doi-asserted-by":"crossref","first-page":"2413","DOI":"10.1007\/s11071-019-05137-9","article-title":"New solitary wave solutions in a perturbed generalized BBM equation","volume":"97","author":"Zhu","year":"2019","journal-title":"Nonlinear Dyn"},{"key":"10.1016\/j.cnsns.2026.109876_bib0025","doi-asserted-by":"crossref","DOI":"10.1142\/S021812742050162X","article-title":"A new type of solitary wave solution of the mKdV equation under singular perturbations","volume":"30","author":"Zhang","year":"2020","journal-title":"Int J Bifurcat Chaos"},{"key":"10.1016\/j.cnsns.2026.109876_bib0026","doi-asserted-by":"crossref","first-page":"3479","DOI":"10.1007\/s11071-021-06975-2","article-title":"New type of solitary wave solution with coexisting crest and trough for a perturbed wave equation","volume":"106","author":"Zhang","year":"2021","journal-title":"Nonlinear Dyn"},{"key":"10.1016\/j.cnsns.2026.109876_bib0027","doi-asserted-by":"crossref","DOI":"10.1016\/j.aml.2021.107668","article-title":"Persistence of solitary wave solutions to a singularly perturbed generalized mKdV equation","volume":"124","author":"Wang","year":"2022","journal-title":"Appl Math Lett"},{"key":"10.1016\/j.cnsns.2026.109876_bib0028","doi-asserted-by":"crossref","first-page":"965","DOI":"10.3934\/dcdsb.2018341","article-title":"Periodic traveling waves in a generalized BBM equation with weak backward diffusion and dissipation terms","volume":"24","author":"Sun","year":"2019","journal-title":"Disc Cont Dyn Syst B"},{"key":"10.1016\/j.cnsns.2026.109876_bib0029","doi-asserted-by":"crossref","first-page":"4689","DOI":"10.3934\/dcds.2020198","article-title":"Existence of periodic waves for a perturbed quintic BBM euqation","volume":"40","author":"Guo","year":"2020","journal-title":"Disc Cont Dyn Syst"},{"key":"10.1016\/j.cnsns.2026.109876_bib0030","doi-asserted-by":"crossref","DOI":"10.1142\/S0218127423500608","article-title":"Periodic waves for a perturbed generalized BBM equation","volume":"33","author":"Dai","year":"2023","journal-title":"Int J Bifurcat Chaos"},{"key":"10.1016\/j.cnsns.2026.109876_bib0031","first-page":"1","article-title":"Existence and uniqueness of periodic waves for a perturbed sixtic generalized BBM equation","volume":"13","author":"Dai","year":"2023","journal-title":"J Appl Anal Comput"},{"key":"10.1016\/j.cnsns.2026.109876_bib0032","doi-asserted-by":"crossref","first-page":"4631","DOI":"10.1007\/s11071-022-08043-9","article-title":"New solitary wave solutions of a generalized BBM equation with distributed delays","volume":"111","author":"Wang","year":"2023","journal-title":"Nonlinear Dyn"},{"key":"10.1016\/j.cnsns.2026.109876_bib0033","doi-asserted-by":"crossref","DOI":"10.1016\/j.physd.2023.133995","article-title":"Traveling waves in a quintic BBM equation under both distributed delay and weak backward diffusion","volume":"458","author":"Fan","year":"2024","journal-title":"Phys D"},{"issue":"08","key":"10.1016\/j.cnsns.2026.109876_bib0034","doi-asserted-by":"crossref","DOI":"10.1142\/S0218127425501019","article-title":"Monotonicity of limit wave speed in the pgKdV equation with nonlinear terms of arbitrarily high degrees","volume":"35","author":"An","year":"2025","journal-title":"Int J Bifurcat Chaos"},{"key":"10.1016\/j.cnsns.2026.109876_bib0035","doi-asserted-by":"crossref","DOI":"10.1016\/j.physd.2025.134656","article-title":"Periodic waves in the pgKdV equation with two arbitrarily high-order nonlinearities","volume":"476","author":"Dai","year":"2025","journal-title":"Phys D"},{"key":"10.1016\/j.cnsns.2026.109876_bib0036","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1007\/s11071-015-1894-7","article-title":"Solitary waves solutions of singularly perturbed higher-order KdV equation via geometric singular perturbation method","volume":"80","author":"Zhuang","year":"2015","journal-title":"Nonlinear Dyn"},{"key":"10.1016\/j.cnsns.2026.109876_bib0037","doi-asserted-by":"crossref","first-page":"988","DOI":"10.1016\/j.jfa.2018.05.005","article-title":"The existence of solitary wave solutions of delayed Camassa-Holm equation via a geometric approach","volume":"275","author":"Du","year":"2018","journal-title":"J Funct Anal"},{"key":"10.1016\/j.cnsns.2026.109876_bib0038","doi-asserted-by":"crossref","first-page":"2961","DOI":"10.3934\/cpaa.2019132","article-title":"Existence results of solitary wave solutions for a delayed Camassa-Holm-KP equation","volume":"18","author":"Li","year":"2019","journal-title":"Commun Pure Appl Anal"},{"key":"10.1016\/j.cnsns.2026.109876_bib0039","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1016\/j.jde.2021.10.033","article-title":"Geometric singular perturbation analysis to Camassa-Holm Kuramoto-Sivashinsky equation","volume":"306","author":"Du","year":"2022","journal-title":"J Differ Equ"},{"issue":"22","key":"10.1016\/j.cnsns.2026.109876_bib0040","first-page":"1","article-title":"Traveling waves in a generalized KdV equation with arbitrarily high-order term and different distributed delays","volume":"24","author":"Wei","year":"2025","journal-title":"Qual Theory Dyn Syst"},{"key":"10.1016\/j.cnsns.2026.109876_bib0041","doi-asserted-by":"crossref","first-page":"1987","DOI":"10.3934\/cpaa.2021118","article-title":"Dynamics of solitary waves and periodic waves for a generalized KP-MEW-Burgers equation with damping","volume":"22","author":"Du","year":"2022","journal-title":"Commun Pure Appl Anal"},{"key":"10.1016\/j.cnsns.2026.109876_bib0042","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0022-0396(79)90152-9","article-title":"Geometric singular perturbation theory for ordinary differential equations","volume":"31","author":"Fenichel","year":"1979","journal-title":"J Differ Equ"},{"key":"10.1016\/j.cnsns.2026.109876_bib0043","first-page":"45","article-title":"Geometric singular perturbation theory","volume":"1609","author":"Jones","year":"1994","journal-title":"Lect Notes Math"},{"key":"10.1016\/j.cnsns.2026.109876_bib0044","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/j.jmaa.2018.04.074","article-title":"New criteria for the monotonicity of the ratio of two Abelian integrals","volume":"465","author":"Liu","year":"2018","journal-title":"J Math Anal Appl"},{"key":"10.1016\/j.cnsns.2026.109876_bib0045","series-title":"Tchebycheff systems: with applications in analysis and statistics","author":"Karlin","year":"1966"},{"key":"10.1016\/j.cnsns.2026.109876_bib0046","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1006\/jdeq.1996.0017","article-title":"A criterion for determining the monotonicity of the ratio of two Abelian integrals","volume":"124","author":"Li","year":"1996","journal-title":"J Differ Equ"},{"key":"10.1016\/j.cnsns.2026.109876_bib0047","doi-asserted-by":"crossref","first-page":"5525","DOI":"10.1090\/S0002-9947-2013-05934-X","article-title":"The monotonicity of the ratio of two Abelian integrals","volume":"365","author":"Liu","year":"2013","journal-title":"Trans Amer Math Soc"},{"key":"10.1016\/j.cnsns.2026.109876_bib0048","doi-asserted-by":"crossref","DOI":"10.1016\/j.aml.2024.109249","article-title":"Periodic wave solutions for a generalized reaction-convection-diffusion equation of high-order","volume":"158","author":"Wei","year":"2024","journal-title":"Appl Math Lett"},{"key":"10.1016\/j.cnsns.2026.109876_bib0049","series-title":"Normal forms, Melnikov functions and bifurcations of limit cycles","author":"Han","year":"2012"},{"key":"10.1016\/j.cnsns.2026.109876_bib0050","first-page":"13","article-title":"The maximum number of zeros of functions with parameters and application to differential equations","volume":"3","author":"Han","year":"2021","journal-title":"J Nonl Mod Anal"},{"key":"10.1016\/j.cnsns.2026.109876_bib0051","series-title":"Differential equations and dynamical systems","author":"Perko","year":"2000"},{"key":"10.1016\/j.cnsns.2026.109876_bib0052","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1016\/j.chaos.2006.09.044","article-title":"Persistence of solitary wave solutions of singularly perturbed Gardner equation","volume":"37","author":"Tang","year":"2008","journal-title":"Chaos Solitons Fractals"},{"key":"10.1016\/j.cnsns.2026.109876_bib0053","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1007\/s10483-009-0411-6","article-title":"Existence of traveling wave solutions for a nonlinear dissipative-dispersive equation","volume":"30","author":"Mansour","year":"2009","journal-title":"Appl Math Mech Engl Ed"},{"key":"10.1016\/j.cnsns.2026.109876_bib0054","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1007\/s12043-009-0148-y","article-title":"Travelling wave solutions for a singularly perturbed Burgers-KdV equation","volume":"73","author":"Mansour","year":"2009","journal-title":"Pramana J Phys"}],"container-title":["Communications in Nonlinear Science and Numerical Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426002364?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1007570426002364?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T03:37:53Z","timestamp":1772941073000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1007570426002364"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8]]},"references-count":54,"alternative-id":["S1007570426002364"],"URL":"https:\/\/doi.org\/10.1016\/j.cnsns.2026.109876","relation":{},"ISSN":["1007-5704"],"issn-type":[{"value":"1007-5704","type":"print"}],"subject":[],"published":{"date-parts":[[2026,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Periodic and solitary waves in a generalized delayed KP-MEW equation with arbitrarily high-order nonlinearity","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.2026.109876","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":"109876"}}