Evolution of complex waves via Davey-Stewartson equation

Yusuf Pandır; Nail Turhan

doi:10.70500/bjs.1666749

EN TR

Evolution of complex waves via Davey-Stewartson equation

Abstract

Davey-Stewartson equations (DSEs) have been discussed to examine the features of wave motion in finite depth water which is affected by gravitational force and surface tension. The new versions of the generalized F-expansion method and the generalized -expansion method are suggested to evaluate the analytical solutions of the DSEs. Thus, single, combined and mixed non-degenerative Jacobi elliptic function solutions (JEFSs) and degenerative solutions of the DSEs are obtained to contribute to the literature. These wave solutions are fresh and unexplored. The visual representations of some solutions are also shown in three and two dimensions.

Keywords

New version of the generalized F-expansion method, New version of the generalized -expansion method, Davey-Stewartson equations, Single combined and mixed JEFSs

References

Ablowitz, M. J., & Clarkson, P. A. (1991). Solitons, nonlinear evolution equations and inverse scattering. Cambridge University Press.
Baojian, H., Dianchen, L., & Fushu, S. (2009). The extended Jacobi elliptic functions expansion method and new exact solutions for the Zakharov equations. World Journal of Modelling Simulation, 3, 216–224.
Cai, G., Wang, Q., & Huang, J. A. (2006). Modified F-expansion method for solving breaking soliton equation. International Journal of Nonlinear Science, 2, 122–128.
Chen, H. T., & Hong-Qing, Z. (2006). New double periodic and multiple soliton solutions of the generalized (2 + 1)-dimensional Boussinesq equation. Chaos, Solitons & Fractals, 20, 765–769. https://doi.org/10.1016/j.chaos.2003.08.006
Chen, Y., & Yan, Z. (2006). The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations. Chaos, Solitons & Fractals, 29, 948–964. https://doi.org/10.1016/j.chaos.2005.08.071
Chuntao, Y. A. (1996). Simple transformation for nonlinear waves. Physics Letters A, 224, 77–84. https://doi.org/10.1016/S0375-9601(96)00770-0
Enam, I. (2010). Generalized Jacobi elliptic function method for traveling wave solutions of (2+1)-dimensional breaking soliton equation. Cankaya University Journal of Science and Engineering, 1, 39–50.
Fan, E. G. (2000). Extended tanh-function method and its applications to nonlinear equations. Physics Letters A, 277, 212–218. https://doi.org/10.1016/S0375-9601(00)00725-8
Feng, Z. S. (2002). On explicit exact solutions to the compound Burgers-KdV equation. Physics Letters A, 293, 57–66. https://doi.org/10.1016/S0375-9601(01)00825-8
Fu, Z., Liu, S., Liu, S., & Zhao, Q. (2001). New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations. Physics Letters A, 290, 72–76. https://doi.org/10.1016/S0375-9601(01)00644-2

Gurefe, Y., Misirli, E., Ekici, M., & Sonmezoglu, A. (2013). Extended trial equation method to generalized nonlinear partial differential equations. Applied Mathematics and Computation, 219(10), 5253–5260. https://doi.org/10.1016/j.amc.2012.11.046
Gurefe, Y., Misirli, E., & Sonmezoglu, A. (2011). Application of trial equation method to the nonlinear partial differential equations arising in mathematical physics. Pramana – Journal of Physics, 77(6), 1023–1029. https://doi.org/10.1007/s12043-011-0201-5
Gurefe, Y., Sonmezoglu, A., & Misirli, E. (2012). Application of an irrational trial equation method to high dimensional nonlinear evolution equations. Journal of Advanced Mathematical Studies, 5(1), 41–47.
Guo, S., & Zhou, Y. (2010). The extended -expansion method and its applications to the Whitham-Broer-Kaup-like equations and coupled Hirota-Satsuma KdV equations. Applied Mathematics and Computation, 215, 3214–3221. https://doi.org/10.1016/j.amc.2009.10.008
He, J. H., & Wu, X. H. (2006). Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals, 30, 700–708. https://doi.org/10.1016/j.chaos.2006.03.020
Inc, M., & Ergut, M. (2005). Periodic wave solutions for the generalized shallow water wave equation by the improved Jacobi elliptic function. Applied Mathematics E-Notes, 5, 89–96.
Liu, C. S. (2005). Trial equation method and its applications to nonlinear evolution equations. Acta Physica Sinica, 54(6), 2505–2509. https://doi.org/10.7498/aps.54.2505
Liu, C. S. (2006). Trial equation method for nonlinear evolution equations with rank inhomogeneous: Mathematical discussions and applications. Communications in Theoretical Physics, 45(2), 219–223. https://doi.org/10.1088/0253-6102/45/2/005
Liu, C. S. (2010). Applications of complete discrimination system for polynomial for classifications of traveling wave solutions to nonlinear differential equations. Computer Physics Communications, 181(2), 317–324. https://doi.org/10.1016/j.cpc.2009.10.006
Liu, S., Fu, S., Liu, S., & Zhao, Q. (2001). Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Physics Letters A, 289, 69–74. https://doi.org/10.1016/S0375-9601(01)00580-1
Lu, H. L., Liu, X. Q., & Niu, L. A. (2010). Generalized -expansion method and its applications to nonlinear evolution equations. Applied Mathematics and Computation, 215(11), 3811–3816. https://doi.org/10.1016/j.amc.2009.11.021
Malanyuk, T. M. (1991). Finite-gap solutions of the Davey-Stewartson II equations. Communications of the Moscow Mathematical Society, 46(5), 193–194.
Malanyuk, T. M. (1994). Finite-gap solutions of the Davey-Stewartson I equations. Journal of Nonlinear Science, 4, 1–21.
Matveev, V. B., & Salle, M. A. (1991). Darboux transformations and solitons. Springer-Verlag.
Pandir, Y. (2014). New exact solutions of the generalized Zakharov-Kuznetsov modified equal-width equation. Pramana – Journal of Physics, 82(6), 949–964. https://doi.org/10.1007/s12043-014-0748-z
Pandir, Y., Gurefe, Y., & Misirli, E. (2013). Classification of exact solutions to the generalized Kadomtsev-Petviashvili equation. Physica Scripta, 87(2), 1–12. https://doi.org/10.1088/0031-8949/87/02/025003
Pandir, Y., Gurefe, Y., & Misirli, E. (2013). The extended trial equation method for some time fractional differential equations. Discrete Dynamics in Nature and Society, 2013, Article ID 491359, 1–8. https://doi.org/10.1155/2013/491359
Pandir, Y., Gurefe, Y., Kadak, U., & Misirli, E. (2012). Classifications of exact solutions for some nonlinear partial differential equations with generalized evolution. Abstract and Applied Analysis, 2012, Article ID 478531, 1–16. https://doi.org/10.1155/2012/478531
Qi, W., Yong, C., & Zhang, H. (2005). A new Jacobi elliptic function rational expansion method and its application to (1+1)-dimensional dispersive long wave equation. Chaos, Solitons & Fractals, 23, 477–483. https://doi.org/10.1016/j.chaos.2004.04.029
Shen, S., & Pan, Z. (2003). A note on the Jacobi elliptic function expansion method. Physics Letters A, 308, 143–148. https://doi.org/10.1016/S0375-9601(02)01802-9
Tajiri, M., & Arai, T. (2010). Periodic soliton solutions to the Davey-Stewartson equation. Proceedings of the Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine, 30(1), 210–217.
Wang, M., Li, X., & Zhang, J. (2008). The -expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Physics Letters A, 372, 417–424. https://doi.org/10.1016/j.physleta.2007.07.051
Wang, M., & Li, X. (2005). Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation. Chaos, Solitons & Fractals, 24, 1257–1268. https://doi.org/10.1016/j.chaos.2004.09.044
Xia, T., & Zhang, S. (2008). An improved generalized F-expansion method and its application to the (2+1)-dimensional KdV equations. Communications in Nonlinear Science and Numerical Simulation, 13, 1294–1301. https://doi.org/10.1016/j.cnsns.2006.12.008
Xia, T. A., & Zhang, S. (2007). Generalized F-expansion method with symbolic computation exactly solving Broer–Kaup equations. Applied Mathematics and Computation, 189, 949–955. https://doi.org/10.1016/j.amc.2006.11.143
Xia, X. Y., Haili, X., & Hongqing, Z. (2012). An extended elliptic equation expansion method and its application in the ZK-MEW equation. International Journal of Nonlinear Science, 3, 316–322.
Xia, X. Y., Haili, X., & Hongqing, Z. (2012). A new extended Jacobi elliptic function expansion method and its application to the generalized shallow water wave equation. Journal of Applied Mathematics, 2012, Article ID 896748, 1–21. https://doi.org/10.1155/2012/896748
Xun, C. (2011). Jacobi elliptic function solutions for (2 + 1) dimensional Boussinesq and Kadomtsev-Petviashvili equation. Applied Mathematics, 2, 1313–1316. https://doi.org/10.4236/am.2011.211183
Yang, K., & Liu, J. (2004). The extended F-expansion method and exact solutions of nonlinear PDEs. Chaos, Solitons & Fractals, 22, 111–121. https://doi.org/10.1016/j.chaos.2003.12.069
Yong, C., Qi, W., & Biao, L. (2004). Jacobi elliptic function rational expansion method with symbolic computation to construct new doubly-periodic solutions of nonlinear evolution equations. Zeitschrift für Naturforschung A, 59a, 529–536. https://doi.org/10.1515/zna-2004-0901
Zhang, J. L., Wang, M. L., Wang, Y. M., & Fang, Z. D. (2006). The improved F-expansion method and its applications. Physics Letters A, 350, 103–109. https://doi.org/10.1016/j.physleta.2005.10.099
Zhang, S., Li, W., Zheng, F., Yu, J., Ji, M., Lu, Z., & Ma, C. A. (2008). Generalized F-expansion method and its application to (2+1)-dimensional breaking soliton equations. International Journal of Nonlinear Science, 5, 25–32.

Details

Primary Language

English

Subjects

Mathematical Methods and Special Functions

Journal Section

Research Article

Authors

Yusuf Pandır ^*
0000-0003-0274-7901
Türkiye

Nail Turhan
0009-0007-9418-2755
Türkiye

Publication Date

May 29, 2025

Submission Date

March 27, 2025

Acceptance Date

May 20, 2025

Published in Issue

Year 2025 Volume: 3 Number: 1

DOI

https://doi.org/10.70500/bjs.1666749

IZ

https://izlik.org/JA46RB36RW

APA

Pandır, Y., & Turhan, N. (2025). Evolution of complex waves via Davey-Stewartson equation. Bozok Journal of Science, 3(1), 42-59. https://doi.org/10.70500/bjs.1666749

AMA

1.Pandır Y, Turhan N. Evolution of complex waves via Davey-Stewartson equation. BJS. 2025;3(1):42-59. doi:10.70500/bjs.1666749

Chicago

Pandır, Yusuf, and Nail Turhan. 2025. “Evolution of Complex Waves via Davey-Stewartson Equation”. Bozok Journal of Science 3 (1): 42-59. https://doi.org/10.70500/bjs.1666749.

EndNote

Pandır Y, Turhan N (May 1, 2025) Evolution of complex waves via Davey-Stewartson equation. Bozok Journal of Science 3 1 42–59.

IEEE

[1]Y. Pandır and N. Turhan, “Evolution of complex waves via Davey-Stewartson equation”, BJS, vol. 3, no. 1, pp. 42–59, May 2025, doi: 10.70500/bjs.1666749.

ISNAD

Pandır, Yusuf - Turhan, Nail. “Evolution of Complex Waves via Davey-Stewartson Equation”. Bozok Journal of Science 3/1 (May 1, 2025): 42-59. https://doi.org/10.70500/bjs.1666749.

JAMA

1.Pandır Y, Turhan N. Evolution of complex waves via Davey-Stewartson equation. BJS. 2025;3:42–59.

MLA

Pandır, Yusuf, and Nail Turhan. “Evolution of Complex Waves via Davey-Stewartson Equation”. Bozok Journal of Science, vol. 3, no. 1, May 2025, pp. 42-59, doi:10.70500/bjs.1666749.

Vancouver

1.Yusuf Pandır, Nail Turhan. Evolution of complex waves via Davey-Stewartson equation. BJS. 2025 May 1;3(1):42-59. doi:10.70500/bjs.1666749

Evolution of complex waves via Davey-Stewartson equation

Evolution of complex waves via Davey-Stewartson equation

Abstract

Keywords

Davey-Stewartson denklemi ile karmaşık dalgaların evrimi

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite