Research Article
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Year 2021, Volume: 70 Issue: 1, 382 - 396, 30.06.2021
https://doi.org/10.31801/cfsuasmas.645030

Abstract

References

  • 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
  • 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
  • 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
  • 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
  • Hirota, R., The direct method in soliton theory, Cambridge University Press, 2004.
  • 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
  • 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
  • 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
  • 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
  • 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
  • Müller, P., Garrett, C., Osborne, A., Rogue waves, Oceanography, 18 (2005), 66-75.
  • Solli, D. R., Ropers, C., Koonath, P., Jalali, B., Optical rogue waves, Nature, 450 (2007), 1054-1057. https://doi.org/10.1038/nature06402
  • 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 equation in fluid dynamics, Int. J. Comput. Math., 96(9) (2019), 1839-1848. https://doi.org/10.1080/00207160.2018.1535708
  • Geng, X., Ma, Y., N-soliton solution and its Wronskian form of a (3+1)-dimensional nonlinear evolution equation, Phys. Lett. A, 369(4) (2007), 285-289. https://doi.org/10.1016/j.physleta.2007.04.099
  • Wu, J-P., A new Wronskian condition for a (3 +1)-dimensional nonlinear evolutions equation, Chin. Phys. Lett., 28(5) (2011), 1-3. https://doi.org/10.1088/0256-307X/28/5/050501
  • Xiao H., Symmetry groups and exact solutions of a (3 + 1)-dimensional nonlinear evolution equation and Maccari's system, Journal of Ningbo University, 24(1) (2011), 108-113.
  • Ma, W. X., Generalized bilinear di¤erential equations, Stud. Nonlinear Sci., 2 (2011), 140-144.
  • Geng, X., Algebraic-geometrical solutions of some multidimensional nonlinear evolution equations, J. Phys. A Math. Theor., 36(9) (2003), 2289. https://doi.org/10.1088/0305- 4470/36/9/307
  • Zhaqilao, Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation, Phys. Lett. A, 377(42) (2013), 3021-3026. https://doi.org/10.1016/j.physleta.2013.09.023
  • Wazwaz, A. M., New (3+1)-dimensional nonlinear evolution equation: multiple soliton solutions, Cent. Eur. J. Eng., 4(4) (2014), 352-356. https://doi.org/10.2478/s13531-013-0173-y
  • Yang, J. Y., Ma, W. X., Abundant lump-type solutions of the Jimbo-Miwa equation in (3+1)-dimensions, Comput. Math. with Appl., 73(2) (2017), 220-225. https://doi.org/10.1016/j.camwa.2016.11.007
  • Zhang, H. Q., Ma, W. X., Lump solutions to the (2+1)-dimensional Sawada-Kotera equation, Nonlinear Dyn., 87(4) (2017), 2305-2310. https://doi.org/10.1007/s11071-016-3190-6
  • Yang, J. Y., Ma, W. X., Qin, Z., Lump and lump-soliton solutions to the (2+1)-dimensional Ito equation, Anal. Math. Phys., 8(3) (2018), 427-436. https://doi.org/10.1007/s13324-017-0181-9
  • Yang, J. Y., Ma, W. X., Khalique, C. M., Determining lump solutions for a combined soliton equation in (2+1)-dimensions, Eur. Phys. J. Plus, 135(6) (2020), 494. https://doi.org/10.1140/epjp/s13360-020-00463-z
  • Ma, W. X., Zhang, Y., Tang, Y., Symbolic computation of lump solutions to a combined equation involving three types of nonlinear terms, East Asian J Appl Math, 10(4) (2020), 732-745. https://doi.org/10.4208/eajam.151019.110420
  • Ma, W. X., Lump and interaction solutions to linear PDEs in 2+1 dimensions via symbolic computation, Mod. Phys. Lett. B, 33(36) (2019), 1950457. https://doi.org/10.1142/S0217984919504578
  • Manafian, J., Lakestani, M., Lump-type solutions and interaction phenomenon to the bidirectional Sawada-Kotera equation, Pramana, 92 (2019), 41. https://doi.org/10.1007/s12043-018-1700-4
  • Manafian, J., Novel solitary wave solutions for the (3+1)-dimensional extended Jimbo-Miwa equations, Comput. Math. with Appl., 76(5) (2018), 1246-1260. https://doi.org/10.1016/j.camwa.2018.06.018
  • Manafian, J., Mohammadi-Ivatloo, B., Abapour, M., Lump-type solutions and interaction phenomenon to the (2+1)-dimensional Breaking Soliton equation, Appl. Math. Comput., 356 (2019), 13-41. https://doi.org/10.1016/j.amc.2019.03.016
  • Manafian, J., Mohammed, S. A., Alizadeh, A. A., Baskonus, H. M., Gao, W., Investigating lump and its interaction for the third-order evolution equation arising propagation of long waves over shallow water, Eur. J. Mech. B Fluids, 84 (2020), 289-301. https://doi.org/10.1016/j.euromechflu.2020.04.013
  • Manafian, J., Lakestani, M., Interaction among a lump, periodic waves, and kink solutions to the fractional generalized CBS-BK equation, Math. Methods Appl. Sci., 44(1) (2021), 1052-1070. https://doi.org/10.1002/mma.6811
  • Manafian, J., Ilhan, O. A., Avazpour, L., Alizadeh, A. A., N-lump and interaction solutions of localized waves to the (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation arise from a model for an incompressible fluid, Math. Methods Appl. Sci., 43(17) (2020), 9904-9927. https://doi.org/10.1002/mma.6665

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

Year 2021, Volume: 70 Issue: 1, 382 - 396, 30.06.2021
https://doi.org/10.31801/cfsuasmas.645030

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.

References

  • 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
  • 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
  • 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
  • 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
  • Hirota, R., The direct method in soliton theory, Cambridge University Press, 2004.
  • 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
  • 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
  • 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
  • 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
  • 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
  • Müller, P., Garrett, C., Osborne, A., Rogue waves, Oceanography, 18 (2005), 66-75.
  • Solli, D. R., Ropers, C., Koonath, P., Jalali, B., Optical rogue waves, Nature, 450 (2007), 1054-1057. https://doi.org/10.1038/nature06402
  • 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 equation in fluid dynamics, Int. J. Comput. Math., 96(9) (2019), 1839-1848. https://doi.org/10.1080/00207160.2018.1535708
  • Geng, X., Ma, Y., N-soliton solution and its Wronskian form of a (3+1)-dimensional nonlinear evolution equation, Phys. Lett. A, 369(4) (2007), 285-289. https://doi.org/10.1016/j.physleta.2007.04.099
  • Wu, J-P., A new Wronskian condition for a (3 +1)-dimensional nonlinear evolutions equation, Chin. Phys. Lett., 28(5) (2011), 1-3. https://doi.org/10.1088/0256-307X/28/5/050501
  • Xiao H., Symmetry groups and exact solutions of a (3 + 1)-dimensional nonlinear evolution equation and Maccari's system, Journal of Ningbo University, 24(1) (2011), 108-113.
  • Ma, W. X., Generalized bilinear di¤erential equations, Stud. Nonlinear Sci., 2 (2011), 140-144.
  • Geng, X., Algebraic-geometrical solutions of some multidimensional nonlinear evolution equations, J. Phys. A Math. Theor., 36(9) (2003), 2289. https://doi.org/10.1088/0305- 4470/36/9/307
  • Zhaqilao, Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation, Phys. Lett. A, 377(42) (2013), 3021-3026. https://doi.org/10.1016/j.physleta.2013.09.023
  • Wazwaz, A. M., New (3+1)-dimensional nonlinear evolution equation: multiple soliton solutions, Cent. Eur. J. Eng., 4(4) (2014), 352-356. https://doi.org/10.2478/s13531-013-0173-y
  • Yang, J. Y., Ma, W. X., Abundant lump-type solutions of the Jimbo-Miwa equation in (3+1)-dimensions, Comput. Math. with Appl., 73(2) (2017), 220-225. https://doi.org/10.1016/j.camwa.2016.11.007
  • Zhang, H. Q., Ma, W. X., Lump solutions to the (2+1)-dimensional Sawada-Kotera equation, Nonlinear Dyn., 87(4) (2017), 2305-2310. https://doi.org/10.1007/s11071-016-3190-6
  • Yang, J. Y., Ma, W. X., Qin, Z., Lump and lump-soliton solutions to the (2+1)-dimensional Ito equation, Anal. Math. Phys., 8(3) (2018), 427-436. https://doi.org/10.1007/s13324-017-0181-9
  • Yang, J. Y., Ma, W. X., Khalique, C. M., Determining lump solutions for a combined soliton equation in (2+1)-dimensions, Eur. Phys. J. Plus, 135(6) (2020), 494. https://doi.org/10.1140/epjp/s13360-020-00463-z
  • Ma, W. X., Zhang, Y., Tang, Y., Symbolic computation of lump solutions to a combined equation involving three types of nonlinear terms, East Asian J Appl Math, 10(4) (2020), 732-745. https://doi.org/10.4208/eajam.151019.110420
  • Ma, W. X., Lump and interaction solutions to linear PDEs in 2+1 dimensions via symbolic computation, Mod. Phys. Lett. B, 33(36) (2019), 1950457. https://doi.org/10.1142/S0217984919504578
  • Manafian, J., Lakestani, M., Lump-type solutions and interaction phenomenon to the bidirectional Sawada-Kotera equation, Pramana, 92 (2019), 41. https://doi.org/10.1007/s12043-018-1700-4
  • Manafian, J., Novel solitary wave solutions for the (3+1)-dimensional extended Jimbo-Miwa equations, Comput. Math. with Appl., 76(5) (2018), 1246-1260. https://doi.org/10.1016/j.camwa.2018.06.018
  • Manafian, J., Mohammadi-Ivatloo, B., Abapour, M., Lump-type solutions and interaction phenomenon to the (2+1)-dimensional Breaking Soliton equation, Appl. Math. Comput., 356 (2019), 13-41. https://doi.org/10.1016/j.amc.2019.03.016
  • Manafian, J., Mohammed, S. A., Alizadeh, A. A., Baskonus, H. M., Gao, W., Investigating lump and its interaction for the third-order evolution equation arising propagation of long waves over shallow water, Eur. J. Mech. B Fluids, 84 (2020), 289-301. https://doi.org/10.1016/j.euromechflu.2020.04.013
  • Manafian, J., Lakestani, M., Interaction among a lump, periodic waves, and kink solutions to the fractional generalized CBS-BK equation, Math. Methods Appl. Sci., 44(1) (2021), 1052-1070. https://doi.org/10.1002/mma.6811
  • Manafian, J., Ilhan, O. A., Avazpour, L., Alizadeh, A. A., N-lump and interaction solutions of localized waves to the (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation arise from a model for an incompressible fluid, Math. Methods Appl. Sci., 43(17) (2020), 9904-9927. https://doi.org/10.1002/mma.6665
There are 33 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Articles
Authors

Yakup Yıldırım 0000-0003-4443-3337

Emrullah Yaşar This is me 0000-0003-4732-5753

Publication Date June 30, 2021
Submission Date November 11, 2019
Acceptance Date February 23, 2021
Published in Issue Year 2021 Volume: 70 Issue: 1

Cite

APA Yıldırım, 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, 70(1), 382-396. https://doi.org/10.31801/cfsuasmas.645030
AMA Yıldırım Y, Yaşar E. Lump-type solutions of a new extended (3+1)-dimensional nonlinear evolution equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2021;70(1):382-396. doi:10.31801/cfsuasmas.645030
Chicago Yıldırım, Yakup, and Emrullah Yaşar. “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 70, no. 1 (June 2021): 382-96. https://doi.org/10.31801/cfsuasmas.645030.
EndNote Yıldırım Y, Yaşar E (June 1, 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 70 1 382–396.
IEEE Y. Yıldırım and E. Yaşar, “Lump-type solutions of a new extended (3+1)-dimensional nonlinear evolution equation”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 1, pp. 382–396, 2021, doi: 10.31801/cfsuasmas.645030.
ISNAD Yıldırım, Yakup - Yaşar, Emrullah. “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 70/1 (June 2021), 382-396. https://doi.org/10.31801/cfsuasmas.645030.
JAMA Yıldırım Y, Yaşar E. Lump-type solutions of a new extended (3+1)-dimensional nonlinear evolution equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:382–396.
MLA Yıldırım, Yakup and Emrullah Yaşar. “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, vol. 70, no. 1, 2021, pp. 382-96, doi:10.31801/cfsuasmas.645030.
Vancouver Yıldırım Y, Yaşar E. Lump-type solutions of a new extended (3+1)-dimensional nonlinear evolution equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(1):382-96.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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