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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2021 / Cilt: 70 - Sayı: 1

Lump-type solutions of a new extended (3+1)-dimensional nonlinear evolution equation

Yakup YILDIRIM
Emrullah YAŞAR
Sayfa
382–396
Yayın Tarihi
2021-06-30
DOI
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Lastly, the graphical simulations of the exact solutions are depicted.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we study lump-type solutions to a new extended (3+1)-dimensional nonlinear evolution equation which appears in the field of wave propagation in the nonlinear systems.
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Temel Bulgular & Veri:We generate these types of solutions by considering the prime number p = 3 of the generalized Hirota bilinear operators.
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Sonuç & Katkı:Lastly, the graphical simulations of the exact solutions are depicted.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Lump-type solution · Generalized bilinear operator · An new extended (3+1)-dimensional nonlinear evolution equation

Abstract

In this paper, we study lump-type solutions to a new extended (3+1)-dimensional nonlinear evolution equation which appears in the field of wave propagation in the nonlinear systems. We generate these types of solutions by considering the prime number p = 3 of the generalized Hirota bilinear operators. With the help of Maple symbolic computations, we retrieve twenty-two classes of lump-type solutions which are a special kind of rational function solutions, localized in all directions in the space and describe various dispersive wave phenomena. These lump-type solutions are derived from positive quadratic function solutions by using the generalized Hirota bilinear form of the considered model. The lump solutions are recovered along with the existence conditions: Analyticity, positivity and localization in all directions. The required conditions of the analyticity and positivity of the solutions can be easily achieved by taking special choices of the involved parameters. The main ingredients for this scheme are to recover the Hirota bilinear forms and their generalized equivalences. Lastly, the graphical simulations of the exact solutions are depicted.

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Bu Makaleye Atıf Yap

YILDIRIM, Y., YAŞAR, E. (2021). Lump-type solutions of a new extended (3+1)-dimensional nonlinear evolution equation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 70 - Sayı: 1, 382–396. https://ajindex.com/articles/746755

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Kaynakça (13)

  1. Seadawy, A. R., Iqbal, M., Lu, D., Construction of soliton solutions of the modify unstable nonlinear Schrödinger dynamical equation in fiber optics, Indian J. Phys., 94(6) (2020), 823-832. https://doi.org/10.1007/s12648-019-01532-5
  2. Lü, D. Z., Cui, Y. Y., Lü, C., Huang, S. Y., New interaction solutions of (3+1)-dimensional Zakharov-Kuznetsov equation, Indian J. Phys, 87(9) (2013), 897-901. https://doi.org/10.1007/s12648-013-0302-8
  3. Sulaiman, T. A., Bulut, H., Yokus, A., Baskonus, H. M., On the exact and numerical solutions to the coupled Boussinesq equation arising in ocean engineering, Indian J. Phys, 93(5) (2019), 647-656. https://doi.org/10.1007/s12648-018-1322-1
  4. Akram, G., Batool, F., A class of traveling wave solutions for space-time fractional biological population model in mathematical physics, Indian J. Phys, 91(10) (2017), 1145-1148. https://doi.org/10.1007/s12648-017-1007-1
  5. Hirota, R., The direct method in soliton theory, Cambridge University Press, 2004.
  6. Wazwaz, A. M., A variety of distinct kinds of multiple soliton solutions for a (3+ 1)-dimensional nonlinear evolution equation, Math. Methods Appl. Sci., 36(3) (2013), 349-357. https://doi.org/10.1002/mma.2600
  7. Ma, W. X., Lump solutions to the Kadomtsev-Petviashvili equation, Phys. Lett. A, 379(36) (2015), 1975-1978. https://doi.org/10.1016/j.physleta.2015.06.061
  8. Ma, W. X., Qin, Z., Lü, X., Lump solutions to dimensionally reduced p-gKP and p-gBKP equations, Nonlinear Dyn., 84(2) (2016), 923-931. https://doi.org/10.1007/s11071-015-2539-6
  9. Lü, X., Chen, S. T., Ma, W. X., Constructing lump solutions to a generalized Kadomtsev-Petviashvili-Boussinesq equation, Nonlinear Dyn., 86(1) (2016), 523-534. https://doi.org/10.1007/s11071-016-2905-z
  10. Ma, W. X., Lump-type solutions to the (3+ 1)-dimensional jimbo-miwa equation, Int. J. Nonlinear Sci. Numer. Simul., 17(7-8) (2016), 355-359. https://doi.org/10.1515/ijnsns-2015- 0050 Yang, J. Y., Ma, W. X., Lump solutions to the BKP equation by symbolic computation, Int. J. Mod. Phys. B, 30(28n29) (2016), 1640028. https://doi.org/10.1142/S0217979216400282
  11. Müller, P., Garrett, C., Osborne, A., Rogue waves, Oceanography, 18 (2005), 66-75.
  12. Solli, D. R., Ropers, C., Koonath, P., Jalali, B., Optical rogue waves, Nature, 450 (2007), 1054-1057. https://doi.org/10.1038/nature06402
  13. Yan, X. W., Tian, S. F., Wang, X. B., Zhang, T. T., Solitons to rogue waves transition, lump solutions and interaction solutions for the (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili