This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Wazwaz AM. Abundant solitons solutions for several forms of the fifth-order KdV equation by using the tanh method. Applied Mathematics and Computation. 2006;182(1):283–300.WazwazAMAbundant solitons solutions for several forms of the fifth-order KdV equation by using the tanh methodApplied Mathematics and Computation20061821283300Search in Google Scholar
Seadawy AR. Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves. Eur. Phys. J. Plus. 2017;132:29. https://doi.org/10.1140/epjp/i2017-11313-4.SeadawyARTravelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water wavesEur. Phys. J. Plus.201713229https://doi.org/10.1140/epjp/i2017-11313-4.Search in Google Scholar
Akram U, Seadawy AR, Rizvi STR, Younis M, Althobaiti S, Sayed S. Traveling wave solutions for the fractional Wazwaz–Benjamin–Bona–Mahony model in arising shallow water waves. Results in Physics. 2021;20:103725. https://doi.org/10.1016/j.rinp.2020.103725AkramUSeadawyARRizviSTRYounisMAlthobaitiSSayedSTraveling wave solutions for the fractional Wazwaz–Benjamin–Bona–Mahony model in arising shallow water wavesResults in Physics.202120103725https://doi.org/10.1016/j.rinp.2020.103725Search in Google Scholar
Rizvi STR, Kashif A, Marwa A. Optical solitons for Biswas–Milovic equation by new extended auxiliary equation method. Optik. 2020;204:164181. https://doi.org/10.1016/j.ijleo.2020.164181RizviSTRKashifAMarwaAOptical solitons for Biswas–Milovic equation by new extended auxiliary equation methodOptik.2020204164181https://doi.org/10.1016/j.ijleo.2020.164181Search in Google Scholar
Seadawy AR. New exact solutions for the KdV equation with higher order nonlinearity by using the variational method. Computers& Mathematics with Applications. 2011; 62(10):2011;3741–3755. https://doi.org/10.1016/j.camwa.2011.09.023SeadawyARNew exact solutions for the KdV equation with higher order nonlinearity by using the variational methodComputers& Mathematics with Applications201162102011;37413755https://doi.org/10.1016/j.camwa.2011.09.023Search in Google Scholar
Asghar A, Seadawy AR, Dianchen L. Soliton solutions of the non-linear Schrödinger equation with the dual power law nonlinearity and resonant nonlinear Schrödinger equation and their modulation instability analysis. Optik. 2017; 145;79–88. https://doi.org/10.1016/j.ijleo.2017.07.016AsgharASeadawyARDianchenLSoliton solutions of the non-linear Schrödinger equation with the dual power law nonlinearity and resonant nonlinear Schrödinger equation and their modulation instability analysisOptik20171457988https://doi.org/10.1016/j.ijleo.2017.07.016Search in Google Scholar
Arshad M, Seadawy AR, Dianchen L. Exact bright–dark solitary wave solutions of the higher-order cubic–quintic nonlinear Schrö-dinger equation and its stability. Optik. 2017;138;40–49. https://doi.org/10.1016/j.ijleo.2017.03.005ArshadMSeadawyARDianchenLExact bright–dark solitary wave solutions of the higher-order cubic–quintic nonlinear Schrö-dinger equation and its stabilityOptik20171384049https://doi.org/10.1016/j.ijleo.2017.03.005Search in Google Scholar
Arnous AH, Seadawy AR, Alqahtani RT, Biswas A. Optical solitons with complex Ginzburg–Landau equation by modified simple equation method. Optik. 2017;144:475–480. https://doi.org/10.1016/j.ijleo.2017.07.013ArnousAHSeadawyARAlqahtaniRTBiswasAOptical solitons with complex Ginzburg–Landau equation by modified simple equation methodOptik2017144475480https://doi.org/10.1016/j.ijleo.2017.07.013Search in Google Scholar
Seadawy AR, El-Rashidy K. Traveling wave solutions for some coupled nonlinear evolution equations, Mathematical and Computer Modelling. 2013;57(5–6):1371–1379. https://doi.org/10.1016/j.mcm.2012.11.026SeadawyAREl-RashidyKTraveling wave solutions for some coupled nonlinear evolution equationsMathematical and Computer Modelling2013575–613711379https://doi.org/10.1016/j.mcm.2012.11.026Search in Google Scholar
Younas U, Younis M, Seadawy AR, Rizvi STR, Althobaiti S, Sayed S. Diverse exact solutions for modified nonlinear Schrödinger equation with conformable fractional derivative. Results in Physics. 2021,20;103766. https://doi.org/10.1016/j.rinp.2020.103766YounasUYounisMSeadawyARRizviSTRAlthobaitiSSayedSDiverse exact solutions for modified nonlinear Schrödinger equation with conformable fractional derivativeResults in Physics202120103766https://doi.org/10.1016/j.rinp.2020.103766Search in Google Scholar
Bhrawy AH, Abdelkawy MA, Kumar S, Biswas A. Solitons and other solutions to Kadomtsev-Petviashvili equation of B-type. Rom. J. Phys. 2013; 58(7–8):729–748.BhrawyAHAbdelkawyMAKumarSBiswasASolitons and other solutions to Kadomtsev-Petviashvili equation of B-typeRom. J. Phys.2013587–8729748Search in Google Scholar
Ebadi G, Fard NY, Bhrawy AH, Kumar S, Triki H, Yildirim A, Biswas A. Solitons and other solutions to the (3+1)-dimensional extended Kadomtsev-Petviashvili equation with power law nonlinearity. Rom. Rep. Phys. 2013; 65(1):27–62.EbadiGFardNYBhrawyAHKumarSTrikiHYildirimABiswasASolitons and other solutions to the (3+1)-dimensional extended Kadomtsev-Petviashvili equation with power law nonlinearityRom. Rep. Phys.20136512762Search in Google Scholar
Iqbal MA, Wang Y, Miah MM, Osman MS. Study on date–Jimbo–Kashiwara–Miwa equation with conformable derivative dependent on time parameter to find the exact dynamic wave solutions. Fractal and Fractional. 2021; 6(1):4.IqbalMAWangYMiahMMOsmanMSStudy on date–Jimbo–Kashiwara–Miwa equation with conformable derivative dependent on time parameter to find the exact dynamic wave solutionsFractal and Fractional2021614Search in Google Scholar
Ali KK, Wazwaz AM, Osman MS. Optical soliton solutions to the generalized nonautonomous nonlinear Schrödinger equations in optical fibers via the sine-Gordon expansion method. Optik. 2020; 208:164132.AliKKWazwazAMOsmanMSOptical soliton solutions to the generalized nonautonomous nonlinear Schrödinger equations in optical fibers via the sine-Gordon expansion methodOptik2020208164132Search in Google Scholar
Akinyemi L, Houwe A, Abbagari S, Wazwaz AM, Alshehri HM, Osman MS. Effects of the higher-order dispersion on solitary waves and modulation instability in a monomode fiber. Optik. 2023; 288: 171202. https://doi.org/10.1016/j.ijleo.2023.171202AkinyemiLHouweAAbbagariSWazwazAMAlshehriHMOsmanMSEffects of the higher-order dispersion on solitary waves and modulation instability in a monomode fiberOptik2023288171202https://doi.org/10.1016/j.ijleo.2023.171202Search in Google Scholar
Mani Rajan MS, Saravana Veni S, Wazwaz AM. Self-steepening nature and nonlinearity management of optical solitons with the influence of generalized external potentials. Opt Quant Electron. 2023; 55:703. https://doi.org/10.1007/s11082-023-04912-8Mani RajanMSSaravana VeniSWazwazAMSelf-steepening nature and nonlinearity management of optical solitons with the influence of generalized external potentialsOpt Quant Electron202355703https://doi.org/10.1007/s11082-023-04912-8Search in Google Scholar
Jafari H, Tajadodi H, Baleanu D. Application of a homogeneous balance method to exact solutions of nonlinear fractional evolution equations. Journal of Computational and Nonlinear Dynamics. 2014;9(2): 021019.JafariHTajadodiHBaleanuDApplication of a homogeneous balance method to exact solutions of nonlinear fractional evolution equationsJournal of Computational and Nonlinear Dynamics201492021019Search in Google Scholar
Kumar S, Malik S, Rezazadeh H, Akinyemi L. The integrable Boussinesq equation and it’s breather, lump and soliton solutions. Nonlinear Dynamics; 2022;1–14.KumarSMalikSRezazadehHAkinyemiLThe integrable Boussinesq equation and it’s breather, lump and soliton solutionsNonlinear Dynamics2022114Search in Google Scholar
Kumar S, Kumar A., Samet B, Gómez-Aguilar JF, Osman MS. A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment. Chaos, Solitons & Fractals 2020; 141: 110321.KumarSKumarA.SametBGómez-AguilarJFOsmanMSA chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatmentChaos, Solitons & Fractals2020141110321Search in Google Scholar
Khan MI, Asghar S, Sabi’u J. Jacobi elliptic function expansion method for the improved modified kortwedge-de vries equation. Optical and Quantum Electronics. 2022; 54: 734.KhanMIAsgharSSabi’uJJacobi elliptic function expansion method for the improved modified kortwedge-de vries equationOptical and Quantum Electronics202254734Search in Google Scholar
Osman MS. One-soliton shaping and inelastic collision between double solitons in the fifth-order variable-coefficient Sawada–Kotera equation. Nonlinear Dynamics. 2019; 96(2):1491–1496.OsmanMSOne-soliton shaping and inelastic collision between double solitons in the fifth-order variable-coefficient Sawada–Kotera equationNonlinear Dynamics201996214911496Search in Google Scholar
Osman MS, Rezazadeh H., Eslami M. Traveling wave solutions for (3+1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity. Nonlinear Engineering. 2016; 8(1):559–567.OsmanMSRezazadehH.EslamiMTraveling wave solutions for (3+1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearityNonlinear Engineering201681559567Search in Google Scholar
Alquran M, Jarrah A. Jacobi elliptic function solutions for a two-mode KdV equation. J King Saud Univ Sci. 2019;31:485–9. https://doi.org/10.1016/j.jksus.2017.06.010AlquranMJarrahAJacobi elliptic function solutions for a two-mode KdV equationJ King Saud Univ Sci2019314859https://doi.org/10.1016/j.jksus.2017.06.010Search in Google Scholar
Jaradat HM, Syam M, Alquran M. A two-mode coupled Korteweg-de Vries: multiple-soliton solutions and other exact solutions. Non-linear Dyn. 2017;90:371–7. https://doi.org/10.1007/s11071-017-3668-xJaradatHMSyamMAlquranMA two-mode coupled Korteweg-de Vries: multiple-soliton solutions and other exact solutionsNon-linear Dyn2017903717https://doi.org/10.1007/s11071-017-3668-xSearch in Google Scholar
Alquran M, Jaradat HM, Syam MI. A modified approach for a reliable study of new nonlinear equation: two-mode Korteweg-de Vries-Burgers equation. Nonlinear Dyn. 2018;91:1619–26. https://doi.org/10.1007/s11071-017-3968-1AlquranMJaradatHMSyamMIA modified approach for a reliable study of new nonlinear equation: two-mode Korteweg-de Vries-Burgers equationNonlinear Dyn201891161926https://doi.org/10.1007/s11071-017-3968-1Search in Google Scholar
Jaradat HM, Awawdeh F, Al-Shara S, Alquran M, Momani S. Controllable dynamical behaviors and the analysis of fractal burgers hierarchy with the full effects of inhomogeneities of media. Rom. J. Phys. 2015; 60:324–43.JaradatHMAwawdehFAl-SharaSAlquranMMomaniSControllable dynamical behaviors and the analysis of fractal burgers hierarchy with the full effects of inhomogeneities of mediaRom. J. Phys.20156032443Search in Google Scholar
Syam M, Jaradat HM, Alquran M. A study on the two-mode coupled modified Korteweg-de Vries using the simplified bilinear and the trigonometric-function methods. Nonlinear Dyn. 2017; 90:1363–71. https://doi.org/10.1007/s11071-017-3732-6SyamMJaradatHMAlquranMA study on the two-mode coupled modified Korteweg-de Vries using the simplified bilinear and the trigonometric-function methodsNonlinear Dyn201790136371https://doi.org/10.1007/s11071-017-3732-6Search in Google Scholar
Alquran M, Jaradat HM, Al-Shara S, Awawdeh F. A new simplified bilinear method for the N-soliton solutions for a generalized F mKdV equation with time-dependent variable coefficients. Int J Nonlinear Sci Numer Simul. 2015;16:259–69. https://doi.org/10.1515/ijnsns-2014-0023AlquranMJaradatHMAl-SharaSAwawdehFA new simplified bilinear method for the N-soliton solutions for a generalized F mKdV equation with time-dependent variable coefficientsInt J Nonlinear Sci Numer Simul20151625969https://doi.org/10.1515/ijnsns-2014-0023Search in Google Scholar
Rezazadeh H, Vahidi J, Zafar A, Bekir A. The functional variable method to find new exact solutions of the nonlinear evolution equations with dual-power-law nonlinearity. Int J Nonlinear Sci Numer Simul. 2020; 21:249–57. https://doi.org/10.1515/ijnsns-2019-0064RezazadehHVahidiJZafarABekirAThe functional variable method to find new exact solutions of the nonlinear evolution equations with dual-power-law nonlinearityInt J Nonlinear Sci Numer Simul20202124957https://doi.org/10.1515/ijnsns-2019-0064Search in Google Scholar
Yépez-Martínez H, Gómez-Aguilar JF. Fractional sub-equation method for Hirota-Satsuma-coupled KdV equation and coupled mKdV equation using the Atangana’s conformable derivative. Waves Ran Comp Med. 2019;29:678–93. https://doi.org/10.1080/17455030.2018.1464233Yépez-MartínezHGómez-AguilarJFFractional sub-equation method for Hirota-Satsuma-coupled KdV equation and coupled mKdV equation using the Atangana’s conformable derivativeWaves Ran Comp Med20192967893https://doi.org/10.1080/17455030.2018.1464233Search in Google Scholar
Yépez-Martínez H, Gómez-Aguilar JF, Baleanu D. Beta-derivative and sub equation method applied to the optical solitons in medium with parabolic law nonlinearity and high order dispersion. Optik. 2018;155:357–65. https://doi.org/10.1016/j.ijleo.2017.10.104Yépez-MartínezHGómez-AguilarJFBaleanuDBeta-derivative and sub equation method applied to the optical solitons in medium with parabolic law nonlinearity and high order dispersionOptik201815535765https://doi.org/10.1016/j.ijleo.2017.10.104Search in Google Scholar
Yépez-Martínez H, Gómez-Aguilar JF. M-derivative applied to the soliton solutions for the Lakshmanan-Porsezian-Daniel equation with dual-dispersion for optical fibers. Optical Quant Electron. 2019; 51:31. https://doi.org/10.1007/s11082-018-1740-5Yépez-MartínezHGómez-AguilarJFM-derivative applied to the soliton solutions for the Lakshmanan-Porsezian-Daniel equation with dual-dispersion for optical fibersOptical Quant Electron20195131https://doi.org/10.1007/s11082-018-1740-5Search in Google Scholar
Akinyemi L. Two improved techniques for the perturbed nonlinear Biswas-Milovic equation and its optical solutions. Optik-International Journal for Light and Electron Optics. 2021;243;167477.AkinyemiLTwo improved techniques for the perturbed nonlinear Biswas-Milovic equation and its optical solutionsOptik-International Journal for Light and Electron Optics2021243167477Search in Google Scholar
Kumar S, Mann N, Kharbanda H, Inc M. Dynamical behavior of analytical soliton solutions, bifurcation analysis, and quasi-periodic solution to the (2+1)-dimensional Konopelchenko–Dubrovsky (KD) system. Analysis and Mathematical Physics. 2023;13(3):40.KumarSMannNKharbandaHIncMDynamical behavior of analytical soliton solutions, bifurcation analysis, and quasi-periodic solution to the (2+1)-dimensional Konopelchenko–Dubrovsky (KD) systemAnalysis and Mathematical Physics202313340Search in Google Scholar
Kumar S, Mann N. A variety of newly formed soliton solutions and patterns of dynamic waveforms for the generalized complex coupled Schrödinger–Boussinesq equations. Optical and Quantum Electronics. 2023;55(8):723.KumarSMannNA variety of newly formed soliton solutions and patterns of dynamic waveforms for the generalized complex coupled Schrödinger–Boussinesq equationsOptical and Quantum Electronics2023558723Search in Google Scholar
Kumar S, Rani S, Mann N. Diverse analytical wave solutions and dynamical behaviors of the new (2+1)-dimensional Sakovich equation emerging in fluid dynamics. The European Physical Journal Plus. 2022;137(11):1226.KumarSRaniSMannNDiverse analytical wave solutions and dynamical behaviors of the new (2+1)-dimensional Sakovich equation emerging in fluid dynamicsThe European Physical Journal Plus2022137111226Search in Google Scholar
Kumar S, Niwas M, Mann N. Abundant analytical closed-form solutions and various solitonic wave forms to the ZK-BBM and GZK-BBM equations in fluids and plasma physics. Partial Differential Equations in Applied Mathematics. 2021;4:100200.KumarSNiwasMMannNAbundant analytical closed-form solutions and various solitonic wave forms to the ZK-BBM and GZK-BBM equations in fluids and plasma physicsPartial Differential Equations in Applied Mathematics.20214100200Search in Google Scholar
Kumar S, Mann N. Abundant closed-form solutions of the (3+1)-dimensional Vakhnenko-Parkes equation describing the dynamics of various solitary waves in ocean engineering. Journal of Ocean Engineering and Science; 2022.KumarSMannNAbundant closed-form solutions of the (3+1)-dimensional Vakhnenko-Parkes equation describing the dynamics of various solitary waves in ocean engineeringJournal of Ocean Engineering and Science2022Search in Google Scholar
Rani S, Kumar S, Mann N. On the dynamics of optical soliton solutions, modulation stability, and various wave structures of a (2+1)-dimensional complex modified Korteweg-de-Vries equation using two integration mathematical methods. Optical and Quantum Electronics. 2023;55(8):731.RaniSKumarSMannNOn the dynamics of optical soliton solutions, modulation stability, and various wave structures of a (2+1)-dimensional complex modified Korteweg-de-Vries equation using two integration mathematical methodsOptical and Quantum Electronics2023558731Search in Google Scholar
Nonlaopon K, Mann N, Kumar S, Rezaei S, Abdou MA. A variety of closed-form solutions, Painlevé analysis, and solitary wave profiles for modified KdV–Zakharov–Kuznetsov equation in (3+1)-dimensions. Results in Physics. 2022;36:105394.NonlaoponKMannNKumarSRezaeiSAbdouMAA variety of closed-form solutions, Painlevé analysis, and solitary wave profiles for modified KdV–Zakharov–Kuznetsov equation in (3+1)-dimensionsResults in Physics.202236105394Search in Google Scholar