On the interaction phenomena to the nonlinear generalized Hietarinta-type equation

doi:10.1016/j.joes.2022.06.027

Abstract

Abstract:

In this paper, we describe the nonlinear behavior of a generalized fourth-order Hietarinta-type equation for dispersive waves in (2 + 1) dimension. The various wave formations are retrieved by using Hirota's bilinear method (HBM) and various test function perspectives. The Hirota method is a widely used and robust mathematical tool for finding soliton solutions of nonlinear partial differential equations (NLPDEs) in a variety of disciplines like mathematical physics, nonlinear dynamics, oceanography, engineering sciences, and others requires bilinearization of nonlinear PDEs. The different wave structures in the forms of new breather, lump-periodic, rogue waves, and two-wave solutions are recovered. In addition, the physical behavior of the acquired solutions is illustrated in three-dimensional, two-dimensional, density, and contour profiles by the assistance of suitable parameters. Based on the obtained results, we can assert that the employed methodology is straightforward, dynamic, highly efficient, and will serve as a valuable tool for discussing complex issues in a diversity of domains specifically ocean and coastal engineering. We have also made an important first step in understanding the structure and physical behavior of complex structures with our findings here. We believe this research is timely and relevant to a wide range of engineering modelers. The results obtained are useful for comprehending the fundamental scenarios of nonlinear sciences.

Key words: Hirota's bilinear method, Lump-periodic solutions, Breather waves, Rouge waves, Multi-waves

Usman Younas, T.A. Sulaiman, Jingli Ren, A. Yusuf. On the interaction phenomena to the nonlinear generalized Hietarinta-type equation[J]. Journal of Ocean Engineering and Science, 2024, 9(1): 89-97.

Usman Younas, T.A. Sulaiman, Jingli Ren, A. Yusuf. [J]. Journal of Ocean Engineering and Science, 2024, 9(1): 89-97.

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URL: https://www.qk.sjtu.edu.cn/joes/EN/10.1016/j.joes.2022.06.027

https://www.qk.sjtu.edu.cn/joes/EN/Y2024/V9/I1/89

Figures/Tables 8

Fig. 1. Plots of solution (8) with parameters

δ_{0} = 0.7, m_{1} = 2.03, ρ_{0} = 2.8, ρ_{1} = 0.72, σ_{0} = - 1.5, y = 0.01

Fig. 1. Plots of solution (8) with parameters $δ_{0} = 0.7, m_{1} = 2.03, ρ_{0} = 2.8, ρ_{1} = 0.72, σ_{0} = - 1.5, y = 0.01$ .

Fig. 2. Plots of solution (12) with parameters

δ_{0} = 1.79, m_{2} = 1.1, m_{1} = 2, ρ_{0} = 1.4, ρ_{1} = 0.65, σ_{0} = 2.01, y = 0.09

Fig. 2. Plots of solution (12) with parameters $δ_{0} = 1.79, m_{2} = 1.1, m_{1} = 2, ρ_{0} = 1.4, ρ_{1} = 0.65, σ_{0} = 2.01, y = 0.09$ .

Fig. 3. Plots of solution (21) with parameters

α_{2} = 0.08, b_{1} = 0.3, b_{2} = 1, γ_{5} = 1.76, q_{2} = 0.6, q_{1} = 0.8, y = 0.99, b_{4} = 0.9, b_{5} = 1.72

Fig. 3. Plots of solution (21) with parameters $α_{2} = 0.08, b_{1} = 0.3, b_{2} = 1, γ_{5} = 1.76, q_{2} = 0.6, q_{1} = 0.8, y = 0.99, b_{4} = 0.9, b_{5} = 1.72$ .

Fig. 4. Plots of solution (25) with parameters

α_{2} = 0.976, b_{1} = 0.7, b_{2} = 1.1, b_{4} = 0.76, q_{2} = 0.9, q_{1} = 1, y = 0.9, b_{3} = 0.7, b_{5} = 1.98

Fig. 4. Plots of solution (25) with parameters $α_{2} = 0.976, b_{1} = 0.7, b_{2} = 1.1, b_{4} = 0.76, q_{2} = 0.9, q_{1} = 1, y = 0.9, b_{3} = 0.7, b_{5} = 1.98$ .

Fig. 5. Plots of solution (30) with parameters

y = 1.8, a_{1} = 1.008, α_{2} = - 0.89, k = 0.9, k_{3} = 0.89, a_{3} = 1.04, a_{6} = - 0.4, k_{2} = 1.3, γ_{3} = 1

Fig. 5. Plots of solution (30) with parameters $y = 1.8, a_{1} = 1.008, α_{2} = - 0.89, k = 0.9, k_{3} = 0.89, a_{3} = 1.04, a_{6} = - 0.4, k_{2} = 1.3, γ_{3} = 1$ .

Fig. 6. Plots of solution (34) with parameters

a_{1} = 2.008, a_{2} = 0.67, α_{2} = 0.7, k = 1.807, k_{3} = 0.78, y = 1.8, a_{3} = 1.09, a_{5} = 2.09, k_{2} = 0.073, γ_{4} = 1.09

Fig. 6. Plots of solution (34) with parameters $a_{1} = 2.008, a_{2} = 0.67, α_{2} = 0.7, k = 1.807, k_{3} = 0.78, y = 1.8, a_{3} = 1.09, a_{5} = 2.09, k_{2} = 0.073, γ_{4} = 1.09$ .

Fig. 7. Plots of solution (39) with parameters

δ_{4} = 0.4, δ_{2} = 1, δ_{3} = - 2, y = 0.01, ϕ_{1} = 0.8

Fig. 7. Plots of solution (39) with parameters $δ_{4} = 0.4, δ_{2} = 1, δ_{3} = - 2, y = 0.01, ϕ_{1} = 0.8$ .

Fig. 8. Plots of solution (43) with parameters

δ_{4} = 2, y = 2, ϕ_{3} = 0.91, ϕ_{2} = 0.02

Fig. 8. Plots of solution (43) with parameters $δ_{4} = 2, y = 2, ϕ_{3} = 0.91, ϕ_{2} = 0.02$ .

References 54

[1]	M.M.A. Khater, S.A. Salama. J. Ocean Eng. Sci., 7 (2022), pp. 264-271
[2]	H. F. Ismael, I. Okumuş, T. Aktürk, H. Bulut, M. S. Osman, J. Ocean Eng. Sci. 10.1016/j.joes.2022.03.017.
[3]	U. Younas, J. Ren, M.Z. Baber, M.W. Yasin, T. Shahzad, J. Ocean Eng. Sci. 10.1016/j.joes.2022.05.005.
[4]	M.M.A. Khater, S.K. Elagan, M.A. El-Shorbagy, S.H. Alfalqi, J.F. Alzaidi, N.A. Alshehri. Commun. Theor. Phys., 73 (2021), p. 095003 DOI: 10.1088/1572-9494/ac049f
[5]	M.M.A. Khater, D. Lu. Mod. Phys. Lett. B, 35 (2021), p. 2150324 DOI: 10.1142/s0217984921503243
[6]	M.M.A. Khater. Mod. Phys. Lett. B, 35 (2021), p. 2150220 DOI: 10.1142/s0217984921502201
[7]	B. Ghanbari, M.S. Osman, D. Baleanu. Mod. Phys. Lett. A, 34 (2019), p. 1950155 DOI: 10.1142/s0217732319501554
[8]	H. Rezazadeh, M.S. Osman, M. Eslami, M. Ekici, A. Sonmezoglu, M. Asma, W.A.M. Othman, B.R. Wong, M. Mirzazadeh, Q. Zhou, A. Biswas, M. Belic. Optik, 164 (2018), pp. 84-92
[9]	U. Younas, J. Ren. Results Phys., 21 (2021), p. 103816
[10]	M.S. Osman, B. Ghanbari. Optik, 175 (2018), pp. 328-333
[11]	K.K. Ali, A.M. Wazwaz, M.S. Osman. Optik, 208 (2020), p. 164132
[12]	M.S. Aktar, M.A. Akbar. Chaos Solitons Fractals, 160 (2022), p. 112212
[13]	M.M.A. Khater. Mod. Phys. Lett. B, 35 (2021), p. 2150372 DOI: 10.1142/s0217984921503723
[14]	M.M.A. Khater. Mod. Phys. Lett. B, 35 (2021), p. 2150456 DOI: 10.1142/s021798492150456x
[15]	M.M.A. Khater. Mod. Phys. Lett. B, 35 (2021), p. 2150480
[16]	U. Younas, T.A. Sulaiman, J. Ren, A. Yusuf. J. Geom. Phys., 178 (2022), p. 104586
[17]	B. Inan, M.S. Osman, T. Ak, D. Baleanu. Math. Methods Appl. Sci., 43 (2020), pp. 2588-2600 DOI: 10.1002/mma.6067
[18]	M. Adel, D. Baleanu, U. Sadiya, M.A. Arefin, M.H. Uddin, M.A. Elamin, M.S. Osman. Results Phy., 38 (2022), p. 105661
[19]	H. Rezazadeh, M. Odabasi, K.U. Tariq, R. Abazari, H.M. Baskonus. Chin. J. Phys., 72 (2021), pp. 403-414
[20]	S. Kumar, S.K. Dhiman, D. Baleanu, M.S. Osman, A.M. Wazwaz. Symmetry, 14 (2022), p. 597
[21]	M.M.A. Khater, K.S. Nisar, M.S. Mohamed. Math. Math. Method App. Sci., 44 (2021), pp. 4598-4606 DOI: 10.1002/mma.7052
[22]	M.M.A. Khater, A.A. Mousa, M.A. El-Shorbagy, R.A.M. Attia. Results Phys., 22 (2021), p. 103954
[23]	M.M.A. Khater, M.S. Mohamed, R.A.M. Attia. Chaos Solitons Fractals, 144 (2021), p. 110676
[24]	M.M.A. Khater, A.E.S. Ahmed, M.A. El-Shorbagy. Results Phys., 22 (2021), p. 103890
[25]	U. Younas, J. Ren. J. Ocean Eng. Sci. (2022), DOI: 10.1016/j.joes.2022.04.014.
[26]	U. Younas, M. Bilal, J. Ren. J. Magn. Magn. Mater., 549 (2020), p. 168995
[27]	K.K. Ali, R. Yilmazer, M.S. Osman. Opt. uant. Electron., 54 (2022), p. 160
[28]	S. Tarla, K.K. Ali, R. Yilmazer, M.S. Osman. Opt Quant Electron, 54 (2022), p. 292
[29]	S. Kumar, R.P. Chauhan, M.S. Osman, S.A. Mohiuddine. Math. Method App. Sci. (2021), DOI: 10.1002/mma.7838.
[30]	U. Younas, M. Bilal, T.A. Sulaiman, J. Ren, A. Yusuf. Opt. Quant. Electron., 54 (2022), p. 71
[31]	M.M.A. Khater, B. Ghanbari. Eur. Phys. J. Plus, 136 (2021), p. 447
[32]	M.M.A. Khater, T.A. Nofal, H. Abu-Zinadah, M.S.M. Lotayif, D. Lu. Alex. Eng. J., 60 (2021), pp. 1797-1806
[33]	M.M.A. Khater, M.S. Mohamed, S.K. Elagan. Results Phys., 23 (2021), p. 104003
[34]	M.M.A. Khater, M.S. Mohamed, S.K. Elagan. Results Phys., 23 (2021), p. 104003
[35]	M.M.A. Khater, S. Anwar, K.U. Tariq, M.S. Mohamed. AIP Adv., 11 (2021), p. 025130
[36]	S.J. Chen, X. Lu, W.X. Ma. Commun. Nonlinear Sci. Numer. Simul., 83 (2020), p. 105135
[37]	U. Younas, J. Ren, T.A. Sulaiman, M. Bilal, A. Yusuf. Mod. Phys. Lett. B (2022), DOI:
[38]	S.T.R. Rizvi, A.R. Seadawy, F. Ashraf, M. Younis, H. Iqbal, D. Baleanu. Eur. Phys. J. Plus, 134 (3) (2019), pp. 1-10 DOI: 10.11114/bms.v5i2.4062
[39]	I. Ahmed, A.R. Seadawy, D. Lu. Int. J. Mod. Phys. B, 33 (2019), p. 1950019
[40]	L. Kaur, A.M. Wazwaz. Phys. Scr., 93 (7) (2018), p. 075203 DOI: 10.1088/1402-4896/aac8b8
[41]	A. Yusuf, T.A. Sulaiman, M. Inc, M. Bayram1. Eur. Phys. J. Plus, 135 (7) (2020), pp. 1-8
[42]	M. Younis, S.T.R. Rizvi, D. Baleanu, H. Iqbal. Chin. J. Phys., 68 (2020), pp. 19-27 DOI: 10.32323/ujma.622495
[43]	C.H. He, Y. Tang, W.X. Ma, J. Ma. Nonlinear Dyn., 95 (2019), pp. 29-42 DOI: 10.1007/s11071-018-4548-8
[44]	M. Singh. Nonlinear Dyn., 84 (2016), pp. 875-880 DOI: 10.1007/s11071-015-2533-z
[45]	J. Manafian, O.A. Ilhan, A. Alizadeh. Math. Methods Appl. Sci. (2020), pp. 1-24
[46]	Y.L. Ma, B.Q. Li. Comput. Math. with Appl., 78 (2019), pp. 827-839
[47]	V.E. Zakharov. Dokl. Akad. Nauk SSSR, 228 (1976), pp. 1314-1316
[48]	A.D.D. Craik, J.A. Adam. Proc. R. Soc. A, 363 (1978), pp. 243-255
[49]	C. Kharif, E. Pelinovsky. Eur. J. Mech. B Fluids, 22 (2003), pp. 603-634
[50]	S. Batwa, W.X. Ma. Front. Math. China, 15 (2020), pp. 435-450 DOI: 10.1007/s11464-020-0844-y
[51]	Y. Feng, S. Bilige. Pramana - J. Phys., 95 (2022), p. 151 DOI: 10.18653/v1/2022.findings-naacl.12
[52]	M.R.A. Fahima, P.R. Kundua, M.E. Islama, M.A. Akbar, M. S. Osman. J. Ocean Eng. Sci., 7 (2022), pp. 272-279
[53]	I. Jaradat, M. Alquran. J. Ocean Eng. Sci., 7 (2022), pp. 244-247
[54]	M.A. Arefin, M.A. Khatun, M.H. Uddin, M. Inc. J. Ocean Eng. Sci., 7 (2022), pp. 292-303

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