Breathers, resonant multiple waves and complexiton solutions of a (2+1)-dimensional nonlinear evolution equation

Sixing Tao; Sixing Tao

doi:10.3934/math.2023590

AIMS Mathematics

2023, Volume 8, Issue 5: 11651-11665. doi: 10.3934/math.2023590

Previous Article Next Article

Research article Special Issues

Breathers, resonant multiple waves and complexiton solutions of a (2+1)-dimensional nonlinear evolution equation

Sixing Tao ^,

School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu, 476000, China

Received: 08 January 2023 Revised: 23 February 2023 Accepted: 28 February 2023 Published: 16 March 2023
MSC : 35A25, 35G50, 35Q35, 37K10

Based on the Hirota bilinear form of a (2+1)-dimensional equation, breathers and resonant multiple waves as well as complexiton solutions are considered in this paper. First, the breather waves are constructed via employing the extend homoclinic test method. By calculation, two kinds of solutions are obtained. Through analysis, three pairs of breathers consisting of hyperbolic functions and trigonometric functions are derived. Furthermore, a rouge wave solution is deduced by applying the Taylor expansion method to a obtained breather wave. In addition, related figures are plotted to illustrate the dynamical features of these obtained solutions. Then, two types of the resonant multi-soliton solutions are obtained by applying the linear superposition principle to the the Hirota bilinear form. At the same time, 3D profiles and 2D density plots are presented to depict the intersection progression of wave motion. Finally, the complexiton solutions are constructed according to the yielded resonant multi-soliton solutions by further utilizing the linear superposition principle. By considering different domain fields, several types of complexiton solutions including the positive ones are derived. Moreover, related 3D and 2D figures are plotted for the obtained results in order to vividly exhibit their dynamics properties.
- exact solutions,
- breather solutions,
- resonant multiple wave solutions,
- linear superposition principle,
- complexiton solutions
Citation: Sixing Tao. Breathers, resonant multiple waves and complexiton solutions of a (2+1)-dimensional nonlinear evolution equation[J]. AIMS Mathematics, 2023, 8(5): 11651-11665. doi: 10.3934/math.2023590

Related Papers:

Abstract

Based on the Hirota bilinear form of a (2+1)-dimensional equation, breathers and resonant multiple waves as well as complexiton solutions are considered in this paper. First, the breather waves are constructed via employing the extend homoclinic test method. By calculation, two kinds of solutions are obtained. Through analysis, three pairs of breathers consisting of hyperbolic functions and trigonometric functions are derived. Furthermore, a rouge wave solution is deduced by applying the Taylor expansion method to a obtained breather wave. In addition, related figures are plotted to illustrate the dynamical features of these obtained solutions. Then, two types of the resonant multi-soliton solutions are obtained by applying the linear superposition principle to the the Hirota bilinear form. At the same time, 3D profiles and 2D density plots are presented to depict the intersection progression of wave motion. Finally, the complexiton solutions are constructed according to the yielded resonant multi-soliton solutions by further utilizing the linear superposition principle. By considering different domain fields, several types of complexiton solutions including the positive ones are derived. Moreover, related 3D and 2D figures are plotted for the obtained results in order to vividly exhibit their dynamics properties.

References

[1]	I. Ali, A. R. Seadawy, S. T. R. Rizvi, M. Younis, K. Ali, Conserved quantities along with Painléve analysis and optical solitons for the nonlinear dynamics of Heisenberg ferromagnetic spin chains model, Int. J. Mod. Phys. B, 34 (2020), 2050283. https://doi.org/10.1142/S0217979220502835 doi: 10.1142/S0217979220502835
[2]	C. Park, R. I. Nuruddeen, K. K. Ali, L. Muhammad, M. S. Osman, D. Baleanu, Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg-de Vries equations, Adv. Differ. Equ., 2020 (2020), 1–12. https://doi.org/10.1186/s13662-020-03087-w doi: 10.1186/s13662-020-03087-w
[3]	K. S. Nisar, O. A. Ilhan, S. T. Abdulazeez, J. Manafian, S. A. Mohammed, M. S. Osman, Novel multiple soliton solutions for some nonlinear PDEs via multiple Exp-function method, Results Phys., 21 (2021), 103769. https://doi.org/10.1016/j.rinp.2020.103769 doi: 10.1016/j.rinp.2020.103769
[4]	I. Ahmed, A. R. Seadawy, D. C. Lu, Kinky breathers, W-shaped and multi-peak solitons interaction in (2 + 1)-dimensional nonlinear Schrödinger equation with Kerr law of nonlinearity, Eur. Phys. J. Plus, 134 (2019), 1–11. https://doi.org/10.1140/epjp/i2019-12482-8 doi: 10.1140/epjp/i2019-12482-8
[5]	J. G. Liu, M. S. Osman, Nonlinear dynamics for different nonautonomous wave structures solutions of a 3D variable-coefficient generalized shallow water wave equation, Chinese J. Phys., 77 (2022), 1618–1624. https://doi.org/10.1016/j.cjph.2021.10.026 doi: 10.1016/j.cjph.2021.10.026
[6]	I. Siddique, M. M. Jaradat, A. Zafar, K. B. Mehdi, M. S. Osman, Exact traveling wave solutions for two prolific conformable M-fractional differential equations via three diverse approaches, Results Phys., 28 (2021), 104557. https://doi.org/10.1016/j.rinp.2021.104557 doi: 10.1016/j.rinp.2021.104557
[7]	Y. Saliou, S. Abbagari, A. Houwe, M. S. Osman, D. S. Yamigno, K. T. Crépin, et al., W-shape bright and several other solutions to the (3+1)-dimensional nonlinear evolution equations, Mod. Phys. Lett. B, 35 (2021), 2150468. https://doi.org/10.1142/S0217984921504686 doi: 10.1142/S0217984921504686
[8]	X. B. Wang, S. F. Tian, C. Y. Qin, T. T. Zhang, Dynamics of the breathers, rogue waves and solitary waves in the (2+1)-dimensional Ito equation, Appl. Math. Lett., 68 (2017), 40–47. https://doi.org/10.1016/j.aml.2016.12.009 doi: 10.1016/j.aml.2016.12.009
[9]	X. W. Yan, S. F. Tian, M. J. Dong, L. Zhou, T. T. Zhang, Characteristics of solitary wave, homoclinic breather wave and rogue wave solutions in a (2+1)-dimensional generalized breaking soliton equation, Comput. Math. Appl., 76 (2018), 179–186. https://doi.org/10.1016/j.camwa.2018.04.013 doi: 10.1016/j.camwa.2018.04.013
[10]	S. X. Tao, Breather wave and traveling wave solutions for a (2 + 1)-dimensional KdV4 equation, Adv. Math. Phys., 2022 (2022), 7761659. https://doi.org/10.1155/2022/7761659 doi: 10.1155/2022/7761659
[11]	L. Kaur, A. M. Wazwaz, Dynamical analysis of lump solutions for (3+1)-dimensional generalized KP-Boussinesq equation and its dimensionally reduced equations, Phys. Scr., 93 (2018), 075203. https://doi.org/10.1088/1402-4896/aac8b8 doi: 10.1088/1402-4896/aac8b8
[12]	Y. F. Zhang, W. X. Ma, J. Y. Yang, A study on lump solutions to a (2+1)-dimensional completely generalized Hirota-Satsuma-Ito equation, Discrete Cont. Dyn.-S, 13 (2020), 2941–2948. https://doi.org/10.3934/dcdss.2020167 doi: 10.3934/dcdss.2020167
[13]	X. Lü, S. J. Chen, G. Z. Liu, W. X. Ma, Study on lump behavior for a new (3+1)-dimensional generalised Kadomtsev-Petviashvili equation, East Asian J. Applied Math., 11 (2021), 594–603. https://doi.org/10.4208/eajam.101120.180221 doi: 10.4208/eajam.101120.180221
[14]	C. K. Kuo, B. Ghanbari, On novel resonant multi-soliton and wave solutions to the (3+1)-dimensional GSWE equation via three effective approaches, Results Phys., 26 (2021), 104421. https://doi.org/10.1016/j.rinp.2021.104421 doi: 10.1016/j.rinp.2021.104421
[15]	S. X. Tao, Breather wave, resonant multi-soliton and M-breather wave solutions for a (3+1)-dimensional nonlinear evolution equation, AIMS Math., 7 (2022), 15795–15811. https://doi.org/10.3934/math.2022864 doi: 10.3934/math.2022864
[16]	N. Raza, M. Kaplan, A. Javid, M. Inc, Complexiton and resonant multi-solitons of a (4+1)-dimensional Boiti-Leon-Manna-Pempinelli equation, Opt. Quantum Electron., 54 (2022), 1–16. https://doi.org/10.1007/s11082-021-03487-6 doi: 10.1007/s11082-021-03487-6
[17]	M. S. Osman, J. A. T. Machado, D. Baleanu, A. Zafar, M. Raheel, On distinctive solitons type solutions for some important nonlinear Schrödinger equations, Opt. Quantum Electron., 53 (2021), 1–24. https://doi.org/10.1007/s11082-020-02711-z doi: 10.1007/s11082-020-02711-z
[18]	M. A. Akbar, F. A. Abdullah, M. T. Islam, M. A. Al Sharif, M. S. Osman, New solutions of the soliton type of shallow water waves and superconductivity models, Results Phys., 44 (2023), 106180. https://doi.org/10.1016/j.rinp.2022.106180 doi: 10.1016/j.rinp.2022.106180
[19]	M. Marin, A. R. Seadawy, S. Vlase, A. Chirila, On mixed problem in thermoelasticity of type III for Cosserat media, J. Taibah Univ. Sci., 16 (2022), 1264–1274. https://doi.org/10.1080/16583655.2022.2160290 doi: 10.1080/16583655.2022.2160290
[20]	M. S. Osman, K. U. Tariq, A. Bekir, A. Elmoasry, N. S. Elazab, M. Younis, et al., Investigation of soliton solutions with different wave structures to the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation, Commun. Theor. Phys., 72 (2020), 7–13. https://doi.org/10.1088/1572-9494/ab6181 doi: 10.1088/1572-9494/ab6181
[21]	S. M. Y. Arafat, K. Fatema, S. M. R. Islam, M. E. Islam, M. A. Akbar, M. S. Osman, The mathematical and wave profile analysis of the Maccari system in nonlinear physical phenomena, Opt. Quantum Electron., 55 (2023), 136. https://doi.org/10.1007/s11082-022-04391-3 doi: 10.1007/s11082-022-04391-3
[22]	Z. D. Dai, J. Liu, D. L. Li, Applications of HTA and EHTA to YTSF Equation, Appl. Math. Comput., 207 (2009), 360–364. https://doi.org/10.1016/j.amc.2008.10.042 doi: 10.1016/j.amc.2008.10.042
[23]	Z. H. Xu, H. L. Chen, Z. D. Dai, Rogue wave for the (2+1)-dimensional Kadomtsev-Petviashvili equation, Appl. Math. Lett., 37 (2014), 34–38. https://doi.org/10.1016/j.aml.2014.05.005 doi: 10.1016/j.aml.2014.05.005
[24]	X. B. Wang, S. F. Tian, C. Y. Qin, T. T. Zhang, Dynamics of the breathers, rogue waves and solitary waves in the (2+1)-dimensional Ito equation, Appl. Math. Lett., 68 (2017), 40–47. https://doi.org/10.1016/j.aml.2016.12.009 doi: 10.1016/j.aml.2016.12.009
[25]	L. Zou, Z. B. Yu, X. B. Wang, Dynamics of the breather waves, rogue waves and solitary waves in an extend Kadomtsev-Petviashvili equation, Appl. Math. Lett., 83 (2018), 73–79. https://doi.org/10.1016/j.aml.2018.03.017 doi: 10.1016/j.aml.2018.03.017
[26]	W. X. Ma, E. G. Fan, Linear superposition principle applying to Hirota bilinear equations, Comput. Math. Appl., 61 (2011), 950–959. https://doi.org/10.1016/j.camwa.2010.12.043 doi: 10.1016/j.camwa.2010.12.043
[27]	F. H. Lin, S. T. Chen, Q. X. Qu, J. P. Wang, X. W. Zhou, X. Lü, Resonant multiple wave solutions to a new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation: Linear superposition principle, Appl. Math. Lett., 78 (2018), 112–117. https://doi.org/10.1016/j.aml.2017.10.013 doi: 10.1016/j.aml.2017.10.013
[28]	C. K. Kuo, W. X. Ma, A study on resonant multi-soliton solutions to the (2+1)-dimensional Hirota-Satsuma-Ito equations via the linear superposition principle, Nonlinear Anal., 190 (2020), 111592. https://doi.org/10.1016/j.na.2019.111592 doi: 10.1016/j.na.2019.111592
[29]	C. K. Kuo, Novel resonant multi-soliton solutions and inelastic interactions to the (3 +1)- and (4 +1)-dimensional Boiti-Leon-Manna-Pempinelli equations via the simplified linear superposition principle, Eur. Phys. J. Plus, 136 (2021), 1–11. https://doi.org/10.1140/epjp/s13360-020-01062-8 doi: 10.1140/epjp/s13360-020-01062-8
[30]	W. X. Ma, Complexiton solutions to the Korteweg-de Vries equation, Phys. Lett. A, 301 (2002), 35–44. https://doi.org/10.1016/S0375-9601(02)00971-4 doi: 10.1016/S0375-9601(02)00971-4
[31]	H. Q. Zhang, W. X. Ma, Extended transformed rational function method and applications to complexiton solutions, Appl. Math. Comput., 230 (2014), 509–515. https://doi.org/10.1016/j.amc.2013.12.156 doi: 10.1016/j.amc.2013.12.156
[32]	J. G. Liu, Y. F. Zhang, I. Muhammad, Resonant soliton and complexiton solutions for (3+1)-dimensional Boiti-Leon-Manna-Pempinell equation, Comput. Math. Appl., 75 (2018), 3939–3945. https://doi.org/10.1016/j.camwa.2018.03.004 doi: 10.1016/j.camwa.2018.03.004
[33]	X. P. Liu, Explicit solutions of the (2+1)-dimensional nonlinear evolution equation, J. Henan Univ. Eng. (In Chinese), 33 (2021), 74–76. https://doi.org/10.3969/j.issn.1674-330X.2021.01.015
[34]	H. C. Ma, A. P. Deng, Lump solution of (2+1)-dimensional Boussinesq equation, Commun. Theor. Phys., 65 (2016), 546–552. https://doi.org/10.1088/0253-6102/65/5/546 doi: 10.1088/0253-6102/65/5/546

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)