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Hosseini, K.; Mirzazadeh, M.; Aligoli, M.; Eslami, M.; Liu, J. G.

Rational wave solutions to a generalized (2+1)-dimensional Hirota bilinear equation. (English) Zbl 1469.37049

Math. Model. Nat. Phenom. 15, Paper No. 61, 12 p. (2020).
Summary: A generalized form of (2+1)-dimensional Hirota bilinear (2D-HB) equation is considered herein in order to study nonlinear waves in fluids and oceans. The present goal is carried out through adopting the simplified Hirota’s method as well as ansatz approaches to retrieve a bunch of rational wave structures from multiple soliton solutions to breather, rational, and complexiton solutions. Some figures corresponding to a series of rational wave structures are provided, illustrating the dynamics of the obtained solutions. The results of the present paper help to reveal the existence of rational wave structures of different types for the 2D-HB equation.

Cited in 10 Documents

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
35C07 Traveling wave solutions
35Q35 PDEs in connection with fluid mechanics

Keywords:

(2+1)-dimensional Hirota bilinear equation; generalized form; simplified Hirota’s method; multiple soliton; breather; rational; complexiton solutions

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[1] A.R. Adem, M. Mirzazadeh, Q. Zhou and K. Hosseini, Multiple soliton solutions of the Sawada-Kotera equation with a nonvanishing boundary condition and the perturbed Korteweg de Vries equation by using the multiple exp-function scheme. Adv. Math. Phys. 2019 (2019) 3175213. · Zbl 1421.35316
[2] X.X. Du, B. Tian and Y. Yin, Lump, mixed lump-kink, breather and rogue waves for a B-type Kadomtsev-Petviashvili equation. Waves Random Complex Media (2019), doi. 10.1080/17455030.2019.1566681. · Zbl 1534.76015
[3] L.L. Feng and T.T. Zhang, Breather wave, rogue wave and solitary wave solutions of a coupled nonlinear Schrödinger equation. Appl. Math. Lett. 78 (2018) 133-140. · Zbl 1384.35119 · doi:10.1016/j.aml.2017.11.011
[4] C.S. Gardner, J.M. Greene, M.D. Kruskal and R.M. Miura, Method for solving the Korteweg-deVries equation. Phys. Rev. Lett. 19 (1967) 1095-1097. · Zbl 1103.35360 · doi:10.1103/PhysRevLett.19.1095
[5] J. He and Y. Li, Designable integrability of the variable coefficient nonlinear Schrödinger equations. Studies Appl. Math. 126 (2011) 1-15. · Zbl 1220.35158 · doi:10.1111/j.1467-9590.2010.00495.x
[6] J. He, L. Wang, L. Li, K. Porsezian and R. Erdlyi, Few-cycle optical rogue waves: Complex modified Korteweg-de Vries equation. Phys. Rev. E 89 (2014) 062917. · doi:10.1103/PhysRevE.89.062917
[7] J.S. He, E.G. Charalampidis, P.G. Kevrekidis and D.J. Frantzeskakis, Rogue waves in nonlinear Schrödinger models with variable coefficients: Application to Bose-Einstein condensates. Phys. Lett. A 378 (2014) 577-583. · Zbl 1331.81100 · doi:10.1016/j.physleta.2013.12.002
[8] J. He, S. Xu and Y. Cheng, The rational solutions of the mixed nonlinear Schrödinger equation. AIP Adv. 5 (2015) 017105. · doi:10.1063/1.4905701
[9] W. Hereman and A. Nuseir, Symbolic methods to construct exact solutions of nonlinear partial differential equations. Math. Comput. Simul. 43 (1997) 13-27. · Zbl 0866.65063 · doi:10.1016/S0378-4754(96)00053-5
[10] W. Hereman and W. Zhuang, Symbolic software for soliton theory. Acta Appl. Math. 39 (1995) 361-378. · Zbl 0838.35111 · doi:10.1007/BF00994643
[11] R. Hirota, The direct method in soliton theory, Cambridge University Press, Cambridge (2004). · Zbl 1099.35111 · doi:10.1017/CBO9780511543043
[12] K. Hosseini, M. Aligoli, M. Mirzazadeh, M. Eslami and J.F. Gómez-Aguilar, Dynamics of rational solutions in a new generalized Kadomtsev-Petviashvili equation. Mod. Phys. Lett. B 33 (2019) 1950437. · doi:10.1142/S0217984919504372
[13] C.C. Hu, B. Tian, H.M. Yin, C.R. Zhang and Z. Zhang, Dark breather waves, dark lump waves and lump wave-soliton interactions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in a fluid. Comput. Math. Appl. 78 (2019) 166-177. · Zbl 1442.35379 · doi:10.1016/j.camwa.2019.02.026
[14] Y.F. Hua, B.L. Guo, W.X. Ma and X. Lü, Interaction behavior associated with a generalized (2+1)-dimensional Hirota bilinear equation for nonlinear waves. Appl. Math. Model. 74 (2019) 184-198. · Zbl 1481.74408 · doi:10.1016/j.apm.2019.04.044
[15] M. Inc, K. Hosseini, M. Samavat, M. Mirzazadeh, M. Eslami, M. Moradi and D. Baleanu, N-wave and other solutions to the B-type Kadomtsev-Petviashvili equation. Ther. Sci. 23 (2019) 2027-2035. · doi:10.2298/TSCI160722367I
[16] J.G. Liu, and Y. He, Abundant lump and lump-kink solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation. Nonlinear Dyn. 92 (2018) 1103-1108. · doi:10.1007/s11071-018-4111-7
[17] J.G. Liu and Q. Ye, Stripe solitons and lump solutions for a generalized Kadomtsev-Petviashvili equation with variable coefficients in fluid mechanics. Nonlinear Dyn. 96 (2019) 23-29. · Zbl 1437.35583 · doi:10.1007/s11071-019-04770-8
[18] J.G. Liu, J.Q. Du, Z.F. Zeng and B. Nie, New three-wave solutions for the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Nonlinear Dyn. 88 (2017) 655-661. · doi:10.1007/s11071-016-3267-2
[19] J.G. Liu, M. Eslami, H. Rezazadeh and M. Mirzazadeh, Rational solutions and lump solutions to a non-isospectral and generalized variable-coefficient Kadomtsev-Petviashvili equation. Nonlinear Dyn. 95 (2019) 1027-1033. · Zbl 1439.35418 · doi:10.1007/s11071-018-4612-4
[20] X. Lü and W.X. Ma, Study of lump dynamics based on a dimensionally reduced Hirota bilinear equation. Nonlinear Dyn. 85 (2016) 1217-1222. · Zbl 1355.35159 · doi:10.1007/s11071-016-2755-8
[21] W.X. Ma and Z. Zhu, Solving the (3+1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm. Appl. Math. Comput. 218 (2012) 11871-11879. · Zbl 1280.35122
[22] W.X. Ma, T. Huang and Y. Zhang, A multiple exp-function method for nonlinear differential equations and its application. Phys. Scr. 82 (2010) 065003. · Zbl 1219.35209 · doi:10.1088/0031-8949/82/06/065003
[23] M.S. Osman and A.M. Wazwaz, A general bilinear form to generate different wave structures of solitons for a (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Math. Methods Appl. Sci. 42 (2019) 6277-6283. · Zbl 1434.35144 · doi:10.1002/mma.5721
[24] M.S. Osman, M. Inc, J.G. Liu, K. Hosseini and A. Yusuf, Different wave structures and stability analysis for the generalized (2+1)-dimensional Camassa-Holm-Kadomtsev-Petviashvili equation. Phys. Scr. 95 (2020) 035229. · doi:10.1088/1402-4896/ab52c1
[25] R. Pouyanmehr, K. Hosseini, R. Ansari and S.H. Alavi, Different wave structures to the (2+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation. Int. J. Appl. Comput. Math. 5 (2019) 149. · Zbl 1428.35100 · doi:10.1007/s40819-019-0730-z
[26] W. Tan, H. Dai, Z. Dai and W. Zhong, Emergence and space-time structure of lump solution to the (2+1)-dimensional generalized KP equation. Pramana J. Phys. 89 (2017) 77. · doi:10.1007/s12043-017-1474-0
[27] A.M. Wazwaz, Multiple-soliton solutions for the generalized (1+1)-dimensional and the generalized (2+1)-dimensional Ito equations. Appl. Math. Comput. 202 (2008) 840-849. · Zbl 1147.65085
[28] A.M. Wazwaz, Multiple-soliton solutions for extended shallow water wave equations. Studies Math. Sci. 1 (2010) 21-29.
[29] A.M. Wazwaz, Two wave mode higher-order modified KdV equations: Essential conditions for multiple soliton solutions to exist. Int. J. Num. Methods Heat Fluid Flow 27 (2017) 2223-2230. · doi:10.1108/HFF-10-2016-0413
[30] A.M. Wazwaz, Multiple complex and multiple real soliton solutions for the integrable sine-Gordon equation. Optik 172 (2018) 622-627. · doi:10.1016/j.ijleo.2018.07.080
[31] A.M. Wazwaz, Multiple complex soliton solutions for the integrable KdV, fifth-order Lax, modified KdV, Burgers, and Sharma-Tasso-Olver equations. Chin. J. Phys. 59 (2019) 372-378. · Zbl 07823539 · doi:10.1016/j.cjph.2019.03.001
[32] A.M. Wazwaz, Multiple complex soliton solutions for integrable negative-order KdV and integrable negative-order modified KdV equations. Appl. Math. Lett. 88 (2019) 1-7. · Zbl 1410.35188 · doi:10.1016/j.aml.2018.08.004
[33] A.M. Wazwaz and L. Kaur, New integrable Boussinesq equations of distinct dimensions with diverse variety of soliton solutions. Nonlinear Dyn. 97 (2019) 83-94. · Zbl 1430.37078 · doi:10.1007/s11071-019-04955-1
[34] R. Zhang, S. Bilige, T. Fang and T. Chaolu, New periodic wave, cross-kink wave and the interaction phenomenon for the Jimbo-Miwa-like equation. Comput. Math. Appl. 78 (2019) 754-764. · Zbl 1442.35406 · doi:10.1016/j.camwa.2019.02.035
[35] Y. Zhou and W.X. Ma, Complexiton solutions to soliton equations by the Hirota method. J. Math. Phys. 58 (2017) 101511. · Zbl 1382.37073 · doi:10.1063/1.4996358
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