Research article

Complexiton solutions and periodic-soliton solutions for the (2+1)-dimensional BLMP equation

  • Received: 29 October 2019 Accepted: 02 December 2019 Published: 04 December 2019
  • MSC : 35C08, 68M07, 33F10

  • The (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation is studied, which describes the incompressible fluid. By virtue of an ansätz functions and the bilinear form, many entirely new complexiton solutions and periodic-soliton solutions are derived. With the aid of symbolic computation, their dynamical behaviors are demonstrated in some three-dimensional plots by choosing different values of the parameters.

    Citation: Jian-Guo Liu, Wen-Hui Zhu, Yan He, Aly R. Seadawy. Complexiton solutions and periodic-soliton solutions for the (2+1)-dimensional BLMP equation[J]. AIMS Mathematics, 2020, 5(1): 421-439. doi: 10.3934/math.2020029

    Related Papers:

  • The (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation is studied, which describes the incompressible fluid. By virtue of an ansätz functions and the bilinear form, many entirely new complexiton solutions and periodic-soliton solutions are derived. With the aid of symbolic computation, their dynamical behaviors are demonstrated in some three-dimensional plots by choosing different values of the parameters.


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    [1] T. Motoda. Time periodic solutions of Cahn-Hilliard systems with dynamic boundary conditions, AIMS Mathematics, 3 (2018), 263-287.
    [2] A. M. Wazwaz. A variety of negative-order integrable KdV equations of higher orders, Wave. Random. Complex., 29 (2019), 195-203.
    [3] W. P. Gao, Y. X. Hu. The exact traveling wave solutions of a class of generalized Black-Scholes equation, AIMS Mathematics, 2 (2017), 385-399.
    [4] Z. F. Zeng, J. G. Liu, Y. Jiang, et al. Transformations and soliton solutions for a variable-coefficient nonlinear schrödinger equation in the dispersion decreasing fiber with symbolic computation, Fund. Inform., 145 (2016), 207-219. doi: 10.3233/FI-2016-1355
    [5] M. T. Islam, M. A. Akbar, M. A. Azad. Traveling wave solutions in closed form for some nonlinear fractional evolution equations related to conformable fractional derivative, AIMS Mathematics, 3 (2018), 625-646.
    [6] W. X. Ma, X. Yong, H. Q. Zhang. Diversity of interaction solutions to the (2+1)-dimensional ito equation, Comput. Math. Appl., 75 (2018), 289-295.
    [7] A. Bashan. An Efficient Approximation to Numerical Solutions for the Kawahara Equation Via Modified Cubic B-Spline Differential Quadrature Method, Mediterr. J. Math., 16 (2019), 14.
    [8] A. Bashan. A novel approach via mixed Crank-Nicolson scheme and differential quadrature method for numerical solutions of solitons of mKdV equation, Pramana, 92 (2019), 84.
    [9] A. Bashan. A mixed algorithm for numerical computation of soliton solutions of the coupled KdV equation: Finite difference method and differential quadrature method, Appl. Math. Comput., 360 (2019), 42-57.
    [10] M. S. Osman. On complex wave solutions governed by the 2d Ginzburg-Landau equation with variable coefficients, Optik, 156 (2018), 169-174.
    [11] Y. H. Yin, W. X. Ma, J. G. Liu, et al. Diversity of exact solutions to a (3+1)-dimensional nonlinear evolution equation and its reduction, Comput. Math. Appl., 76 (2018), 1275-1283. doi: 10.1016/j.camwa.2018.06.020
    [12] Y. Kong, L. Xin, Q. Qiu, et al. Exact periodic wave solutions for the modified Zakharov equations with a quantum correction, Appl. Math. Lett., 94 (2019), 140-148. doi: 10.1016/j.aml.2019.01.009
    [13] Y. Z. Li, J. G. Liu. Multiple periodic-soliton solutions of the (3 + 1)-dimensional generalised shallow water equation, Pramana, 90 (2018), 71.
    [14] W. X. Ma, Y. Zhou. Lump solutions to nonlinear partial differential equations via Hirota bilinear forms, J. Differ. Equations., 264 (2018), 2633-2659.
    [15] G. Akram, F. Batool. Solitary wave solutions of the Schafer-Wayne short-pulse equation using two reliable methods, Opt. Quant. Electron., 49 (2017), 14.
    [16] J. Y. Yang, W. X. Ma, Z. Y. Qin. Lump and lump-soliton solutions to the (2+1)-dimensional Ito equation, Anal. Math. Phys., 8 (2018), 427-436.
    [17] Z. Z. Lan. Rogue wave solutions for a coupled nonlinear Schrödinger equation in the birefringent optical fiber, Appl. Math. Lett., 98 (2019), 128-134.
    [18] L. N. Gao, X. Y. Zhao, Y. Y. Zi, et al. esonant behavior of multiple wave solutions to a Hirota bilinear equation, Comput. Math. Appl., 72 (2016), 1225-1229. doi: 10.1016/j.camwa.2016.06.008
    [19] A. M. Wazwaz. A study on a (2+1)-dimensional and a (3+1)-dimensional generalized Burgers equation, Appl. Math. Lett., 31 (2014), 41-45.
    [20] J. G. Liu. Double-periodic soliton solutions for the (3+1)-dimensional Boiti-Leon-MannaPempinelli equation in incompressible fluid, Comput. Math. Appl., 75 (2018), 3604-3613.
    [21] Y. F. Hua, B. L. Guo, W. X. Ma, et al. Interaction behavior associated with a generalized (2+1)- dimensional Hirota bilinear equation for nonlinear waves, Appl. Math. Model., 74 (2019), 184-198. doi: 10.1016/j.apm.2019.04.044
    [22] X. P. Zeng, Z. D. Dai, D. L. Li. New periodic soliton solutions for the (3 + 1)-dimensional potentialYTSF equation, Chaos. Soliton. Fract., 42 (2009), 657-661.
    [23] O. Gonzalez-Gaxiola. Bright and dark optical solitons of the Schafer-Wayne short-pulse equation by Laplace substitution method, Optik, 200 (2020), 163414.
    [24] J. G. Liu, J. Q. Du, Z. F. Zeng, et al. Exact periodic cross-kink wave solutions for the new (2+1) dimensional kdv equation in fluid flows and plasma physics, Chaos, 26 (2016), 989-1002.
    [25] A. M. Wazwaz. Multiple complex and multiple real soliton solutions for the integrable sine-Gordon equation, Optik, 172 (2018), 622-627.
    [26] Y. N. Tang, W. J. Zai. New periodic-wave solutions for (2+1)- and (3+1)-dimensional Boiti-LeonManna-Pempinelli equations, Nonlinear Dyn., 81 (2015), 249-255.
    [27] L. Luo. New exact solutions and Bäklund transformation for Boiti-Leon-Manna-Pempinelli equation, Phys. Lett. A., 375 (2001), 1059-1063.
    [28] S. H. Ma, J. P. Fang. Multi dromion-solitoff and fractal excitations for (2+1)-dimensional BoitiLeon-Manna-Pempinelli system, Commun. Theor. Phys., 52 (2009), 641-645.
    [29] L. Delisle, M. Mosaddeghi. Classical and SUSY solutions of the Boiti-Leon-Manna-Pempinelli equation, J. Phys. A Math. Theor., 46 (2013), 115203.
    [30] M. Najafi, M. Najafi, S. Arbabi. Wronskian determinant solutions of the (2+1)-dimensional BoitiLeon-Manna-Pempinelli equation, Int. J. Adv. Math. Sci., 1 (2013), 8-11.
    [31] Z. H. Fu, J. G. Liu. Exact periodic cross-kink wave solutions for the (2+1)-dimensional Boiti-LeonManna-Pempinelli equation, Indian. J. Pure. Ap. Phy., 55 (2017), 163-167.
    [32] Y. Li, D. S. Li. New exact solutions for the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation, Appl. Math. Sci., 6 (2012), 579-587.
    [33] K. Melike, A. Arzu, B. Ahmet. The Auto-Bäcklund transformations for the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation, AIP Conference Proceedings, 1798 (2017), 020071.
    [34] K. Melike. Two different systematic techniques to find analytical solutions of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation, Chinese J. Phys., 56 (2018), 2523-2530.
    [35] C. J. Bai, H. Zhao. New solitary wave and jacobi periodic wave excitations in (2+1)-demensional Boiti-Leon-Manna-Pempinelli system, Int. J. Mod. Phys. B, 22 (2008), 2407-2420.
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