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International Journal of Frontiers in Sociology, 2021, 3(13); doi: 10.25236/IJFS.2021.031315.

Rogue Wave Solutions of the (3+1)-Dimensional Generalized Kadomtsev-Petviashvili Equation

Author(s)

Fu-Fu Ge

Corresponding Author:
Fu-Fu Ge
Affiliation(s)

Foundation Department, Xuzhou Vocational College of Industrial Technology, Xuzhou 221140, People's Republic of China

Abstract

The rogue wave solutions of the (3+1)-dimensional generalized Kadomtsev-Petviashvili (gKP) equation are constructed by Hirota bilinear method and symbolic computation approach. By choosing proper polynomial function, the first, the second and the third order rogue wave solutions are systematically obtained. The maximum amplitude and the minimum amplitude of the first order rogue wave solution are given. Moreover, the first three order generalised rogue wave solutions are also explicitly presented. Finally, some features of rogue wave solutions are graphically discussed.

Keywords

The generalized Kadomtsev-Petviashvili equation, Symbolic computation approach, Rogue wave solution, Generalised rogue wave solution

Cite This Paper

Fu-Fu Ge. Rogue Wave Solutions of the (3+1)-Dimensional Generalized Kadomtsev-Petviashvili Equation. International Journal of Frontiers in Sociology (2021), Vol. 3, Issue 13: 95-105. https://doi.org/10.25236/IJFS.2021.031315.

References

[1] E. Pelinovsky and C. Kharif(Editors), "Extreme Ocean Waves," Second Edition, Springer (2016).

[2] R. Grimshaw, E. Pelinovsky, T. Taipova, A. Sergeeva, Rogue internal waves in the ocean: long wave model, Eur. Phys. J. Spec. Top. 185 (2010) 195-208.

[3] D.R. Solli, C. Ropers, P. Koonath, B. Jalali, Optical rogue waves, Nature 450 (2007) 1045-1057.

[4] B. Kibler, J. Fatome, C. Finot, et al, The Peregrine soliton in nonlinear fibre optics, Nat. Phys. 6(10) (2010) 790-795.

[5] D.W. Zuo, Y.T. Gao, L. Xue, Y.J. Feng, Y.H. Sun, Rogue waves for the generalized nonlinear SchrÖingder-Maxwell-Bloch system in optical-fiber communication, Appl. Math. Lett. 40 (2015) 78-83.

[6] P.S. Vinayagam, R. Radha, K. Porszian, Taming rogue waves in Vector BECs, Phys. Rev. A 88 (2013) 042906.

[7] L.C. Zhao, Dynamics of nonautonomous rogue waves in Bose-Einstein condensate, Ann. Phys. 329 (2013) 73-79.

[8] J.S. He, E.G. Charalampidis, P.G. Kevrekidis, D.J. Frantzeskakis, Rogue waves in nonlinear SchrÖdinger models with variable coefficients: application to Bose-Einstein condensates, Phys. Lett. A 378(5-6) (2014) 577-583.

[9] Z.Y. Yan, Financial rogue waves, Commun. Theor. Phys. 54(5) (2010) 947-949.

[10] Z.Y. Yan, Vector financial rogue waves, Phys. Lett. A 375(48) (2011) 4274-4279.

[11] N. Akhmediv, A. Ankiewicz, M. Taki, Waves that appear from nowhere and disappear without a trace, Phys. Lett. A 373 (2009) 675-678.

[12] N. Akhmediev, J.M. Soto-Crespo and A. Ankiewicz, Extreme waves that appear from nowhere: on the nature of rogue waves, Phys. Lett. A 373 (2009) 2137-2145.

[13] A. Ankiewicz, D.J. Kedziora, N. Akhmediev, Controllable rogue waves in the nonautonomous nonlinear system with a linear potential, Phys. Lett. A 375 (2011) 2782.

[14] D.H. Peregrine, Water waves nonlinear SchrÖding equations and their solutions, Math. Soc. B, App. Math. 25 (1983) 16-43.

[15] S.W. Xu, J.S. He, The rogue wave and breather solution of the Gerdjikov-Ivanov equation, J. Math. Phys. 53 (2012) 063507.

[16] L.H. Wang, K. Porsezian, J.S. He, Breather and rogue wave solutions of a generalized nonlinear SchrÖdinger equation, Phys. Rev. E 87 (2013) 053202.

[17] Zhaqilao, On Nth-order rogue wave solution to the generalized nonlinear SchrÖdinger equation, Phys. Lett. A 377(12) (2013) 855-859.

[18] A. Ankiewicz, J.M. Soto-Crespo, N. Akhmediev, Rogue waves and rational solutions of the Hirota equation, Phys. Rev. E 81 (2010) 046602.

[19] J.S. He, S.W. Xu, K. Porsezian, Rogue waves of the Fokas-Lenells equation, J. Phys. Soc. Jpn. 81 (2012) 124007.

[20] B.L. Guo, L.M. Ling, Rogue wave, breathers and Bright-Dark-Rogue solutions for the Coupled SchrÖdinger equations, Chin. Phys. Lett. 28(11) (2011) 4-7.

[21] W.Q. Peng, S.F. Tian, T.T. Zhang, Dynamics of breather waves and higher-order rogue waves in a coupled nonlinear SchrÖdinger equation. EPL, 123 (2018) 50005.

[22] L.L. Feng, S.F. Tian, X.B. Wang, T.T. Zhang, Rogue waves, homoclinic breather waves and soliton waves for the (2+1)-dimensional B-type Kadomtsev-Petviashvili equation, Appl. Math. Lett. 65 (2017) 90-97.

[23] W.Q. Peng, S.F. Tian, T.T. Zhang, Analysis on lump, lumpoff and rogue waves with predictability to the (2+1)-dimensional B-type Kadomtsev-Petviashvili equation, Phys. Lett. A 241 (2018) 1-8.

[24] C.Y. Qin, S.F. Tian, X.B. Wang, T.T. Zhang, J. Li, Rogue waves, bright-dark solitons and traveling wave solutions of the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation, Comput. Math. Appl. 75 (2018) 4221–4231.

[25] M.J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform. SIAM, USA: Philadephia, 1981.

[26] M.J. Ablowitz, P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering. Cambrige: Cambrige Univ.  Press 1991.

[27] R. Hirota, Direct methods in soliton theory. Springer-Verlag Berlin Heideberg, 1980.

[28] V.B. Matveev, M.A. Salli, Darboux Transformations and Solitons, Springer Series in Nonlinear Dynamics. Berlin: Sprige Press 1991.

[29] C. Rogers, W.F. Shadwick,  B$\ddot{\rm a}$cklund transformations and their applications. Academic Press, New York-London 1982.

[30] S.Y. Lou, L.L. Chen, Formally variable separation approach for nonintegrable models, J. Math. Phys. 40 (1999) 6491-6500.

[31] G.W. Bluman, S. Kumei, Symmetries and Differential Equations, New York: Springer Verlag, 1989.

[32] P.A. Clarkson, E. Dowie, Rational solutions of the Boussinesq equation and applications to rogue waves, Trans. Math. Appl. 1 (2017) 1-26.

[33] W.X. Ma, Lump solutions to the Kadomtsev-Petviashhvili equation, Phys. Lett. A 379(36) (2015) 1975-1978.

[34] J.J. Guo, J.S. He, M.H. Li, D. Mihalache, Multiple-order line rogue wave solutions of extended Kadomtsev-Petviashhvili equation, Math. Comput. Simulat. 180 (2021) 251-257.

[35] Zhaqilao, A symbolic computation approach to constructing rogue waves with a controllable center in the nonlinear systems, Comput. Math. Appl. 75(9) (2018) 3331-3342.

[36] B.Q. Li, Y.L. Ma, Multiple-lump waves for a (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation arising from incompressible fluid, Comput. Math. Appl. 76 (2018) 204-214.

[37] Z.L. Zhao, L.C. He, Multiple lump solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation, Appl. Math. Lett. 95 (2019) 114-121.

[38] W.H. Liu, Y.F. Zhang, Multiple rogue wave solutions of the (3+1)-dimensional Kadomtsev-Petviashhvili-Boussinesq equation, Z. Angew. Math. Phys. 70 (2019) 112.

[39] S.F. Tian, P.L. Ma, On the Quasi-Periodic wave solutions and asymptotic ananlysis to a (3+1)-dimensional generalized Kadomtsev-Petviashhvili equation, Commun. Theor. Phys. 62 (2014) 245-258.