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Abstrakty
The complex method is systematic and powerful to build various kinds of exact meromorphic solutions for nonlinear partial differential equations on the complex plane C. By using the complex method, abundant new exact meromorphic solutions to the (2 + 1)-dimensional and the (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equations and the (2 + 1)-dimension Kundu-Mukherjee-Naskar equation are investigated. Abundant new elliptic solutions, rational solutions and exponential solutions have been constructed.
Wydawca
Czasopismo
Rocznik
Tom
Strony
129--139
Opis fizyczny
Bibliogr. 31 poz., rys.
Twórcy
autor
- School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China
Bibliografia
- [1] S. Zhang, C. Tian, and W. Qian, Bilinearization and new multisoliton solutions for the (4+1)-dimensional Fokas equation, Pramana 86(2016), no. 6, 1259-1267, DOI: https://doi.org/10.1007/s12043-015-1173-7.
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- [3] M. A. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, Cambridge, 1991.
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- [5] C. Rogers and W. Schief, Bäcklund and Darboux Transformations: Geometry and Modern Applications in Soliton Theory, Cambridge University Press, Cambridge, 2002.
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- [7] S. Liu, Z. Fu, S. Liu, and Q. Zhao, Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations, Phys. Lett. A 289(2001), no. 1-2, 69-74, DOI: https://doi.org/10.1016/S0375-9601(01)00580-1.
- [8] M. F. El-Sabbagh and A. T. Ali, New generalized Jacobi elliptic function expansion method, Commun. Nonlinear Sci. Numer. Simul. 13(2008), no. 9, 1758-1766, DOI: https://doi.org/10.1016/j.cnsns.2007.04.014.
- [9] M. Wang, X. Li, and J. Zhang, The G′∕G-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Phys. Lett. A 372(2008), no. 4, 417-423, DOI: https://doi.org/10.1016/j.physleta.2007.07.051.
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- [11] J. He and X. Wu, Exp-function method for nonlinear wave equations, Chaos, Solitons Fractals 30(2006), no. 3, 700-708,DOI: https://doi.org/10.1016/j.chaos.2006.03.020.
- [12] G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, 1994.
- [13] A. J. M. Jawad, M. D. Petković, and A. Biswas, Modified simple equation method for nonlinear evolution equations, Appl. Math. Comput. 217(2010), no. 2, 869-877, DOI: https://doi.org/10.1016/j.amc.2010.06.030.
- [14] K. Hosseini, Z. Ayati, and R. Ansari, New exact traveling wave solutions of the Tzitzéica type equations using a novel exponential rational function method, Optik 148(2017), 85-89, DOI: https://doi.org/10.1016/j.ijleo.2017.08.030.
- [15] M. Mirzazadeh, Y. Yıldırım, E. Yaşar, H. Triki, Q. Zhou, S. P. Moshokoa, et al., Optical solitons and conservation law of Kundu-Eckhaus equation, Optik 154(2018), 551-557, DOI: https://doi.org/10.1016/j.ijleo.2017.10.084.
- [16] A. Biswas, Y. Yıldırım, E. Yaşar, Q. Zhou, S. P. Moshokoa, and M. Belic, Optical solitons for Lakshmanan-Porsezian-Daniel model by modified simple equation method, Optik 160(2018), 24-32, DOI: https://doi.org/10.1016/j.ijleo.2018.01.100.
- [17] Y. S. Özkan, E. Yaşar, and A. R. Seadawy, A third-order nonlinear Schrödinger equation: the exact solutions, group-invariant solutions and conservation laws, J. Taibah Univ. Sci. 14(2020), no. 1, 585-597,DOI: https://doi.org/10.1080/16583655.2020.1760513.
- [18] Y. Tang and W. Zai, New periodic-wave solutions for (2 + 1)- and (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equations, Nonlinear Dyn. 81(2015), 249-255, DOI: https://doi.org/10.1007/s11071-015-1986-4.
- [19] M. Kaplan, Two different systematic techniques to find analytical solutions of the (2 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation, Chinese J. Phys. 56(2018), no. 5, 2523-2530, DOI: https://doi.org/10.1016/j.cjph.2018.06.005.
- [20] W. Yuan, Y. Li, and J. Lin, Meromorphic solutions of an auxiliary ordinary differential equation using complex method, Math. Methods Appl. Sci. 36(2013), no. 13, 1776-1782, DOI: https://doi.org/10.1002/mma.2723.
- [21] W. Yuan, Y. Wu, Q. Chen, and Y. Huang, All meromorphic solutions for two forms of odd order algebraic differential equations and its applications, Appl. Math. Comput. 240(2014), 240-251, DOI: https://doi.org/10.1016/j.amc.2014.04.099.
- [22] Y. Huang, W. Yuan, and Y. Wu, All traveling wave exact solutions of two kinds of nonlinear evolution equations, Appl. Math. Comput. 235(2014), 148-156, DOI: https://doi.org/10.1016/j.amc.2014.02.071.
- [23] Y. Gu, W. Yuan, N. Aminakbari, and J. Lin, Meromorphic solutions of some algebraic differential equations related Painlevé equation IV and its applications, Math. Methods Appl. Sci. 41(2018), no. 10, 3832-3840, DOI: https://doi.org/10.1002/mma.4869.
- [24] M. Ekici, A. Sonmezoglu, A. Biswas, and M. R. Belic, Optical solitons in (2 + 1)-dimensions with Kundu-Mukherjee-Naskar equation by extended trial function scheme, Chinese J. Phys. 57(2019), 72-77, DOI: https://doi.org/10.1016/j.cjph.2018.12.011.
- [25] A. Biswas, Y. Yıldırım, E. Yaşar, Q. Zhou, S. P. Moshokoa, and A. Belic, Optical soliton perturbation with quadratic-cubic nonlinearity using a couple of strategic algorithms, Chinese J. Phys. 56(2018), no. 5, 1990-1998, DOI: https://doi.org/10.1016/j.cjph.2018.09.009.
- [26] D. Qiu, Y. Zhang, and J. He, The rogue wave solutions of a new (2 + 1)-dimensional equation, Commun. Nonlinear Sci. Numer. Simul. 30(2016), no. 1-3, 307-315, DOI: https://doi.org/10.1016/j.cnsns.2015.06.025.
- [27] A. Eremenko, Meromorphic traveling wave solutions of the Kuramoto-Sivashinsky equation, J. Math. Phys. Anal. Geom. 2(2006), no. 3, 278-286.
- [28] S. Lang, Elliptic Functions, Springer-Verlag, New York, 1987.
- [29] R. Conte and M. Musette, Elliptic general analytic solutions, Stud. Appl. Math. 123(2009), no. 1, 63-81, DOI: https://doi.org/10.1111/j.1467-9590.2009.00447.x.
- [30] A. Eremenko, Meromorphic solutions of equations of briot-bouquet type, Teor. Funktsii Funktsional. Anali: Prilozhen 127(1982), no. 38, 48-56.
- [31] A. Eremenko, L. Liao, and T. Ng, Meromorphic solutions of higher order briotbouquet differential equations, Math. Proc. Cambridge Philos. Soc. 146(2009), no. 1, 197-206, DOI: https://doi.org/10.1017/S030500410800176X.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-10c99e20-4ea6-4b6f-af56-f816a8ab0c2c