Research article

Extractions of some new travelling wave solutions to the conformable Date-Jimbo-Kashiwara-Miwa equation

  • Received: 20 October 2020 Accepted: 07 January 2021 Published: 07 February 2021
  • MSC : 35Axx, 33Dxx

  • In this paper, complex and combined dark-bright characteristic properties of nonlinear Date-Jimbo-Kashiwara-Miwa equation with conformable are extracted by using two powerful analytical approaches. Many graphical representations such as 2D, 3D and contour are also reported. Finally, general conclusions of about the novel findings are introduced at the end of this manuscript.

    Citation: Ajay Kumar, Esin Ilhan, Armando Ciancio, Gulnur Yel, Haci Mehmet Baskonus. Extractions of some new travelling wave solutions to the conformable Date-Jimbo-Kashiwara-Miwa equation[J]. AIMS Mathematics, 2021, 6(5): 4238-4264. doi: 10.3934/math.2021251

    Related Papers:

  • In this paper, complex and combined dark-bright characteristic properties of nonlinear Date-Jimbo-Kashiwara-Miwa equation with conformable are extracted by using two powerful analytical approaches. Many graphical representations such as 2D, 3D and contour are also reported. Finally, general conclusions of about the novel findings are introduced at the end of this manuscript.


    [1] H. Rezazadeh, A. Korkmaz, M. Eslami, J. Vahidi, R. Asghari, Traveling wave solution of conformable fractional generalized reaction Duffing model by generalized projective Riccati equation method, Opt. Quant. Electron, 50 (2018), 1-13. doi: 10.1007/s11082-017-1266-2
    [2] J. L. G.Guirao, H. M. Baskonus, A. Kumar, M. S. Rawat, G. Yel, Complex Patterns to the (3+1)-Dimensional B-type Kadomtsev-Petviashvili-Boussinesq Equation, Symmetry, 12 (2020), 17.
    [3] J. L. G. Guirao, H. M. Baskonus, A. Kumar, F. S. V. Causanilles, G. R. Bermudez, Complex mixed dark-bright wave patterns to the modified alpha and modified Vakhnenko-Parkes equations, Alexandria Eng. J., 59 (2020), 2149-2160. doi: 10.1016/j.aej.2020.01.032
    [4] W. Gao, B. Ghanbari, H. Günerhan, H. M. Baskonus, Some mixed trigonometric complex soliton solutions to the perturbed nonlinear Schrödinger equation, Modern Physics Letters B, 34 (2020), 2050034.
    [5] H. M. Baskonus, New acoustic wave behaviors to the Davey-Stewartson equation with power-law nonlinearity arising in fluid dynamics, Nonlinear Dyn., 86 (2016), 177-183. doi: 10.1007/s11071-016-2880-4
    [6] H. Bulut, T. A. Sulaiman, H. M. Baskonus, New solitary and optical wave structures to the Korteweg-de Vries equation with dual-power law nonlinearity, Opt Quant Electron, 48 (2016) 1-14.
    [7] H. M. Baskonus, T. A. Sulaiman, H. Bulut, New Solitary Wave Solutions to the (2+1)-Dimensional Calogero-Bogoyavlenskii-Schi and the Kadomtsev-Petviashvili Hierarchy Equations, Indian J. Phys., 91 (2017), 1237-1243. doi: 10.1007/s12648-017-1033-z
    [8] R. Khalil, M. A. Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014), 6570.
    [9] T. A. Sulaiman, G. Yel, H. Bulut, M-fractional solitons and periodic wave solutions to the Hirota Maccari system, Mod. Phys. Lett. B, 33 (2019), 1950052.
    [10] M. Eslami, F. S. Khodadad, F. Nazari, H. Rezazadeh, The first integral method applied to the Bogoyavlenskii equations by means of conformable fractional derivative, Opt. Quant. Electron., 49 (2017), 1-18. doi: 10.1007/s11082-016-0848-8
    [11] H. Bulut, T. A. Sulaiman, H. M. Baskonus, H. Rezazadeh, M. Eslami, M. Mirzazadeh, Optical solitons and other solutions to the conformable space-time fractional Fokas-Lenells equation, Optik, 172 (2018), 20-27. doi: 10.1016/j.ijleo.2018.06.108
    [12] J. L. G. Guirao, H. M. Baskonus, A. Kumar, Regarding new wave patterns of the Newly Extended Nonlinear (2+1)-Dimensional Boussinesq Equation with Fourth Order, Mathematics, 8 (2020), 1-9.
    [13] M. S. Osman, H. Rezazadeh, M. Eslami, Traveling wave solutions for (3+1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity, Nonlinear Engineering, 8 (2019), 559-567. doi: 10.1515/nleng-2018-0163
    [14] W. Gao, G. Yel, H. M. Baskonus, C. Cattani, Complex Solitons in the Conformable (2+1)-dimensional Ablowitz-Kaup-Newell-Segur Equation, Aims Math., 5 (2020), 507-521. doi: 10.3934/math.2020034
    [15] W. Gao, P. Veeresha, D. G. Prakasha, H. M. Baskonus, G. Yel, New Numerical Results for the Time-Fractional Phi-Four Equation Using a Novel Analytical Approach, Symmetry, 12 (2020), 1-16.
    [16] E. I. Eskitascioglu, M. B. Aktas, H. M. Baskonus, New Complex and Hyperbolic Forms for Ablowitz-Kaup-Newell-Segur Wave Equation with Fourth Order, Applied Mathematics and Nonlinear Sciences, 4 (2019), 105-112.
    [17] D. Kumar, J. Singh, S. D. Purohit, R. Swroop, A hybrid analytical algorithm for nonlinear fractional wave-like equations, Mathematical Modelling of Natural Phenomena, 14 (2019), 304. doi: 10.1051/mmnp/2018063
    [18] T. A. Sulaiman, H. Bulut, Optical solitons and modulation instability analysis of the (2+1)-dimensional coupled nonlinear Schrödinger equation, Commun. Theor. Phys., 72 (2020), 1-6.
    [19] H. M. Baskonus, A. Kumar, A. Kumar, W. Gao, Deeper investigations of the (4 + 1)-dimensional Fokas and (2 + 1)-dimensional Breaking soliton equations, Int. J. Modern Physics B, 34 (2020), 2050152. doi: 10.1142/S0217979220501520
    [20] F. Guo, J. Lin, Interaction solutions between lump and stripe soliton to the (2+ 1)-dimensional Date-Jimbo-Kashiwara-Miwa equation, Nonlinear Dyn., 96 (2019), 1233-1274. doi: 10.1007/s11071-019-04850-9
    [21] B. B. Kadomtsev, V. I. Petviashvili, On the stability of solitary waves in weakly dispersive media, Sov. Phys. Dokl., 15 (1970), 539–541.
    [22] E. Date, M. Jimbo, M. Kashiwara, T. Miwa, A new hierarchy of soliton equations of KP-type, Physica D, 4 (1981), 343–365.
    [23] M. Singh, R. K. Gupta, On Painleve analysis, symmetry group and conservation laws of Date-Jimbo-Kashiwara-Miwa equation, Int. J. Appl. Comput. Math., 4 (2018), 88.
    [24] H. F. Ismael, H. Bulut, C. Park, M. S. Osman, M-lump, N-soliton solutions, and the collision phenomena for the (2 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa equation, Results Phys., 19 (2020), 103329.
    [25] J. G. Liu, W. H. Zhu, M. S. Osman, W. X. Ma, An explicit plethora of different classes of interactive lump solutions for an extension form of 3D-Jimbo-Miwa model, Eur. Phys. J. Plus, 135 (2020), 412. doi: 10.1140/epjp/s13360-020-00405-9
    [26] A. M. Wazwaz, A (2+1)-dimensional time-dependent Date–Jimbo–Kashiwara–Miwa equation: Painlevé integrability and multiple soliton solutions, Comput. Math. Appl., 79 (2020), 1145-1149. doi: 10.1016/j.camwa.2019.08.025
    [27] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014), 65-70. doi: 10.1016/
    [28] G. Yel, H. M. Baskonus, W. Gao, New Dark-Bright Soliton in the Shallow Water wave Model, AIMS Math., 5 (2020), 4027–4044. doi: 10.3934/math.2020318
    [29] S. Guo, L. Mei, Y. Li, Y. Sun, The improved fractional sub-equation method and its applications to the space-time fractional differential equations in fluid mechanics, Phys. Lett. A, 376 (2012), 407-411. doi: 10.1016/j.physleta.2011.10.056
    [30] H. Bulut, G. Yel, H. M. Baskonus, An Application of Improved Bernoulli Sub-Equation Function Method to The Nonlinear Time-Fractional Burgers Equation, Turk. J. Math. Comput. Sci., 5 (2016), 1-7.
    [31] E. Ihan, I. O. Kiymaz, A generalization of truncated M-fractional derivative and applications to fractional differential equations, Appl. Math. Nonlin. Sciences, 5 (2020), 171–188. doi: 10.2478/amns.2020.1.00016
    [32] H. Durur, E. Ilhan, H. Bulut, Novel Complex Wave Solutions of the (2+1)-Dimensional Hyperbolic Nonlinear Schrödinger Equation, Fractal and Fractional, 4 (2020), 41. doi: 10.3390/fractalfract4030041
    [33] A. R. Seadawy, Stability analysis solutions for nonlinear three-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation in a magnetized electron-positron plasma, Physica A, 455 (2016), 44–51. doi: 10.1016/j.physa.2016.02.061
    [34] C. Cattani, A review on Harmonic Wavelets and their fractional extension, J. Advanced Engineering and Computation, 2 (2018), 224-238.
    [35] A. R. Seadawy, Ion acoustic solitary wave solutions of two-dimensional nonlinear adomtsev–Petviashvili–Burgers equation in quantum plasma, Mathematical methods and applied Sciences, 40 (2017), 1598–1607.
    [36] X. J. Yang, M. A. Aty, C. Cattani, A new general fractional order derivative with Rabotnov fractional -exponential kernel applied to model the anomalous heat, Therm. Sci., 23 (2019), 1677-1681. doi: 10.2298/TSCI180320239Y
    [37] A. R. Seadawy, Stability analysis of traveling wave solutions for generalized coupled nonlinear KdV equations, Appl. Math. Inf. Sci., 10 (2016), 209-214. doi: 10.18576/amis/100120
    [38] A. R. Seadawy, Three-dimensional nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma, Comput. Math. Appl., 71 (2016), 201–212. doi: 10.1016/j.camwa.2015.11.006
    [39] A. Ciancio, A. Quartarone, A hybrid model for tumor-immune competition, U.P.B. Sci. Bull., series A, 75 (2013), 125-136.
    [40] A. R. Seadawy, Nonlinear wave solutions of the three-dimensional Zakharov–Kuznetsov–Burgers equation in dusty plasma, Physica A, 439 (2015), 124–131. doi: 10.1016/j.physa.2015.07.025
    [41] R. M. Jena, S. Chakraverty, D. Baleanu, A novel analytical technique for the solution of time-fractional Ivancevic option pricing model, Physica A, 550 (2020), 15.
    [42] M. Z. Sarikaya, C. C. Bilisik, Some generalizations of Opial type inequalities for conformable fractional integrals, Progress in Fractional Differentiation and Applications, 6 (2020), 137-142. doi: 10.18576/pfda/060206
    [43] A. R. Seadawy, Stability analysis for two-dimensional ion-acoustic waves in quantum plasmas, Physics of Plasmas, 21 (2014), 052107. doi: 10.1063/1.4875987
    [44] R. Agarwal, M. P. Yadav, R. P. Agarwal, D. Baleanu, Analytic solution of space time fractional advection dispersion equation with retardation for contaminant transport in porous media, Progress in Fractional Differentiation and Applications, 5 (2019), 283-295.
    [45] K. Hosseini, M. Samavat, M. Mirzazadeh, W. X. Ma, Z. Hammouch, A New (3+1)-dimensional Hirota Bilinear Equation: Its Bäcklund Transformation and Rational-type Solutions. Regular and Chaotic Dynamics, 25 (2020), 383-391.
    [46] A. Houwe, J. Sabi'u, Z. Hammouch, S. Y. Doka, Solitary pulses of a conformable nonlinear differential equation governing wave propagation in low-pass electrical transmission line. Physica Scripta, 95 (2020), 045203.
    [47] M. F. Uddin, M. G. Hafez, Z. Hammouch, D. Baleanu, Periodic and rogue waves for Heisenberg models of ferromagnetic spin chains with fractional beta derivative evolution and obliqueness, Waves in Random and Complex Media, (2020), 1-15
    [48] K. S. Al-Ghafri, H. Rezazadeh, Solitons and other solutions of (3 + 1)-dimensional space–time fractional modified KdV–Zakharov–Kuznetsov equation, Appl. Math. Nonlin. Sciences, 4 (2019), 289–304. doi: 10.2478/AMNS.2019.2.00026
    [49] M. M. Khader, K. M. Saad, Z. Hammouch, D. Baleanu, A spectral collocation method for solving fractional KdV and KdV-Burger's equations with non-singular kernel derivatives, Appl. Numer. Math., 161 (2021), 137-146. doi: 10.1016/j.apnum.2020.10.024
    [50] A. R. Seadawy, Modulation instability analysis for the generalized derivative higher order nonlinear Schrödinger equation and its the bright and dark soliton solutions, J. Electromagnetic Waves and Applications, 31 (2017), 1353-1362. doi: 10.1080/09205071.2017.1348262
    [51] A. Yokus, S. Gulbahar, Numerical Solutions with Linearization Techniques of the Fractional Harry Dym Equation, Appl. Math. Nonlin. Sciences, 4 (2019), 35–42. doi: 10.2478/AMNS.2019.1.00004
    [52] A. R. Seadawy, The generalized nonlinear higher order of KdV equations fromthe higher order nonlinear Schrodinger equation and its solutions, Optik, 139 (2017), 31-43. doi: 10.1016/j.ijleo.2017.03.086
    [53] B. Ghanbari, J. F. Gómez-Aguilar, New exact optical soliton solutions for nonlinear Schrödinger equation with second-order spatio-Temporal dispersion involving M-derivative, Modern Physics Letters B, 33 (2019), 1950235.
    [54] B. Ghanbari, D. Baleanu, New Solutions of Gardner's Equation Using Two Analytical Methods, Frontiers in Physics, 2019.
    [55] A. R. Seadawy, Travelling wave solutions of a weakly nonlinear two-dimensional higher order Kadomtsev-Petviashvili dynamical equation for dispersive shallow water waves, European Physical J. Plus, 132 (2017), 1-13. doi: 10.1140/epjp/i2017-11280-8
    [56] J. P. Yu, Y. L. Sun, Lump solutions to dimensionally reduced Kadomtsev–Petviashvili-like equations, Nonlinear Dyn., 87 (2017), 1405-1412. doi: 10.1007/s11071-016-3122-5
    [57] N. N. Kadkhoda, H. Jafari, An analytical approach to obtain exact solutions of some space-time conformable fractional differential equations, Adv. Differ. Equ., 2019 (2019), 428. doi: 10.1186/s13662-019-2349-0
    [58] R. Jiwari, V. Kumar, S. Singh, Lie group analysis, exact solutions and conservation laws to compressible isentropic Navier–Stokes equation, Engineering with Computers, 2020.
    [59] J. P. Yu, Y. L. Sun, A note on the Gaussons of some new logarithmic evolution equations, Comput. Math. Appl., 74 (2017), 258-265. doi: 10.1016/j.camwa.2017.04.014
    [60] A. R. Seadawy, K. El-Rashidy, Traveling wave solutions for some coupled nonlinear evolution equations by using the direct algebraic method, Math. Comput. Model., 57 (2013), 1371–1379.
    [61] A. Yokus, T. A. Sulaiman, H. M. Baskonus, S. P. Atmaca, On the exact and numerical solutions to a nonlinear model arising in mathematical biology, ITM Web of Conferences, 22 (2018), 1-10, .
    [62] J. Singh, D. Kumar, Z. Hammouch, A. Atangana, A fractional epidemiological model for computer viruses pertaining to a new fractional derivative, Appl. Math. Comput., 316 (2018), 504-515.
    [63] A. R. Seadawy, Stability analysis for Zakharov-Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma, Comp. Math. Appl., 67 (2014), 172-180. doi: 10.1016/j.camwa.2013.11.001
    [64] V. Kumar, A. M. Wazwaz, Lie symmetry analysis and soliton solutions for complex short pulse equation, Waves in Random and Complex Media, 2020.
    [65] X. J. Yang, D. Baleanu, F. Gao, New analytical solutions for Klein-Gordon and Helmholtz equations in fractal dimensional space, Proc. Rom. Acad., Ser. A: Math. Phys. Tech. Sci. Inf. Sci 18 (2017), 231-238.
    [66] M. Yavuz, N. Sene, Approximate solutions of the model describing fluid flow using generalized ρ-laplace transform method and heat balance integral method, Axioms, 9 (2020), 123. doi: 10.3390/axioms9040123
    [67] V. Kumar, R. K. Gupta, R. Jiwari, Comparative study of travelling-wave and numerical solutions for the coupled short pulse (CSP) equation, Chinese Phys. B, 22 (2013), 050201. doi: 10.1088/1674-1056/22/5/050201
    [68] J. P. Yu, Y. L.Sun, Study of lump solutions to dimensionally reduced generalized KP equations, Nonlinear Dyn., 87 (2017), 2755-2763. doi: 10.1007/s11071-016-3225-z
    [69] Y. L. Sun, W. X. Ma, J. P. Yu, C. M. Khalique, Dynamics of lump solitary wave of Kadomtsev– Petviashvili–Boussinesq-like equation, Comput. Math. Appl., 78 (2019), 840-847. doi: 10.1016/j.camwa.2019.03.001
    [70] J. P. Yu, Y. L. Sun, A direct Bäcklund transformation for a (3+1)-dimensional Kadomtsev– Petviashvili–Boussinesq-like equation, Nonlinear Dyn., 90 (2017), 2263-2268. doi: 10.1007/s11071-017-3799-0
    [71] J. P. Yu, Y. L. Sun, F. D. Wang, N-soliton solutions and long-time asymptotic analysis for a generalized complex Hirota–Satsuma coupled KdV equation, Appl. Math. Lett., 106 (2020), 106370. doi: 10.1016/j.aml.2020.106370
    [72] R. Hirota, Direct Methods in Soliton Theory, Solitons, 1980.
    [73] J. P. Yu, F. Wang, W. X. Ma, Y. L. Sun, Chaudry Masood Khalique, Multiple-soliton solutions and lumps of a (3+1)-dimensional generalized KP equation, Nonlinear Dyn., 25 (2019), 1687-1692.
    [74] G. Yel, New wave patterns to the doubly dispersive equation in nonlinear dynamic elasticity, Pramana J. Phys., 94 (2020), 79. doi: 10.1007/s12043-020-1941-x
    [75] H. M. Baskonus, C. Cattani, A. Ciancio, Periodic, Complex and Kink-type Solitons for the Nonlinear Model in Microtubules, Appl. Sci., 21 (2019), 34-45.
    [76] E. W. Weisstein, Concise Encyclopedia of Mathematics, CRC Press, New York, 2002.
  • Reader Comments
  • © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (
通讯作者: 陈斌,
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索


Article views(2913) PDF downloads(359) Cited by(32)

Article outline

Figures and Tables



DownLoad:  Full-Size Img  PowerPoint