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On solving the (3+1)-dimensional B-type Kadomtsev-Petviashvili equation by using two efficient method

Yıl 2025, Cilt: 29 Sayı: 1, 54 - 61, 25.04.2025

Mustafa Ekici

https://doi.org/10.19113/sdufenbed.1611725

Öz

This paper employs two distinct yet potent methodologies in order to tackle the intricate difficulties posed by nonlinear partial differential equations. Our primary focus is on deriving novel exact solutions for the (3+1)-dimensional B-type Kadomtsev-Petviashvili equation. The (3+1)-dimensional B-type Kadomtsev-Petviashvili equation serves as the focal point of this research. By employing the unified method and the generalized Kudryashov method, solitary wave solutions for this equation are obtained. These methods not only contribute to the theoretical analysis of nonlinear systems but also facilitate a deeper understanding of multidimensional wave phenomena. The newly derived exact solutions provide significant insights into the physical interpretations of these equations, paving the way for advanced applications in fields such as energy transmission, signal processing, and wave dynamics. This work highlights the effectiveness of these methodologies and their potential to enhance both the theoretical and practical understanding of nonlinear phenomena.

Anahtar Kelimeler

The generalized Kudryashov method B-type Kadomtsev-Petviashvili equation Unified method

Kaynakça

  • [1] Sun, Y., Tian, B., Liu, L., 2017. Rogue waves and lump solitons of the (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation for water waves. Commun. Theor. Phys. 68(6), 693.
  • [2] Odibat, Z., and Momani, S. 2008. A generalized differential transform method for linear partial differential equations of fractional order. Applied Mathematics Letters, 21(2), 194-199.
  • [3] Ekici, M., Ayaz, F. 2017. Solution of model equation of completely passive natural convection by improved differential transform method. Research on Engineering Structures and Materials, 3(1), 1-10.
  • [4] El-Sayed, A. M. A., Gaber, M. 2006. The Adomian decomposition method for solving partial differential equations of fractal order in finite domains. Physics Letters A, 359(3), 175-182.
  • [5] El-Sayed, A. M. A., Behiry, S. H., Raslan, W. E. 2010. Adomian's decomposition method for solving an intermediate fractional advection–dispersion equation. Computers & Mathematics with Applications, 59(5), 1759-1765.
  • [6] Kaplan, M., Bekir, A., Akbulut, A. 2016. A generalized Kudryashov method to some nonlinear evolution equations in mathematical physics. Nonlinear Dynamics, 85, 2843-2850.
  • [7] Zhang, S., Tong, J. L., and Wang, W. 2008. A generalized-expansion method for the mKdV equation with variable coefficients. Physics Letters A, 372(13), 2254-2257.
  • [8] Ekici, M., Ünal, M. 2022. Application of the rational (G'/G)-expansion method for solving some coupled and combined wave equations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(1), 116-132.
  • [9] Ünal M., Ekici, M. 2021. The Double (G'/G, 1/G)-Expansion Method and Its Applications for Some Nonlinear Partial Differential Equations. Journal of the Institute of Science and Technology, 11(1), 599-608.
  • [10] Isah, M. A., Yokus, A. 2022. Application of the newly φ^6− model expansion approach to the nonlinear reaction-diffusion equation. Open J. Math. Sci, 6, 269-280.
  • [11] Fan, E. 2000. Extended tanh-function method and its applications to nonlinear equations. Physics Letters A, 277(4), 212-218.
  • [12] Zhang, J. L., Wang, M. L., and Li, X. Z. 2006. The subsidiary ordinary differential equations and the exact solutions of the higher order dispersive nonlinear Schrödinger equation. Physics Letters A, 357(3), 188-195.
  • [13] Wang, M., Li, X., Zhang, J. 2007. Various exact solutions of nonlinear Schrödinger equation with two nonlinear terms. Chaos, Solitons & Fractals, 31(3), 594-601.
  • [14] Ekici M. Exact Solutions of Time-Fractional Thin-Film Ferroelectric Material Equation with Conformable Fractional Derivative. BSJ Eng. Sci. 2025;8(1):179-84.
  • [15] Muhammad, T., Hamoud, A. A., Emadifar, H., Hamasalh, F. K., Azizi, H., Khademi, M. 2022. Traveling wave solutions to the Boussinesq equation via Sardar sub-equation technique. AIMS Mathematics, 7(6), 11134-11149.
  • [16] He, J. H., and Wu, X. H. 2006. Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals, 30(3), 700-708.
  • [17] Ekici, M., Ünal, M. 2020. Application of the exponential rational function method to some fractional soliton equations. In Emerging Applications of Differential Equations and Game Theory (pp. 13-32). IGI Global.
  • [18] Zhang, S., and Zhang, H. Q. 2011. Fractional sub-equation method and its applications to nonlinear fractional PDEs. Physics Letters A, 375(7), 1069-1073.
  • [19] Ekici, M. (2023). Exact solutions to some nonlinear time-fractional evolution equations using the generalized Kudryashov method in mathematical physics. Symmetry, 15(10), 1961.
  • [20] Kadomtsev, B. B., Petviashvili, V. I. (1970). On the stability of solitary waves in weakly dispersing media. In Doklady Akademii Nauk (Vol. 192, No. 4, pp. 753-756). Russian Academy of Sciences.
  • [21] Ablowitz, M. J., Clarkson, P. A. (1991). Solitons, nonlinear evolution equations and inverse scattering (Vol. 149). Cambridge university press.
  • [22] Hirota, R. (2004). The direct method in soliton theory (No. 155). Cambridge University Press.
  • [23] Jimbo, M., Miwa, T. (1983). Solitons and infinite dimensional Lie algebras. Publications of the Research Institute for Mathematical Sciences, 19(3), 943-1001.
  • [24] Dickey, L. A. (2003). Soliton equations and Hamiltonian systems (Vol. 26). World scientific.
  • [25] Takasaki, K., Takebe, T. (1995). Integrable hierarchies and dispersionless limit. Reviews in Mathematical Physics, 7(5), 743-808.
  • [26] Wazwaz, A. M. 2024. Study on a (3+ 1)-dimensional B-type Kadomtsev-Petviashvili equation in nonlinear physics: Multiple soliton solutions, lump solutions, and breather wave solutions. Chaos, Solitons and Fractals, 189, 115668.
  • [27] Wazwaz, A. M. (2013). Two B-type Kadomtsev-Petviashvili equations of (2+ 1) and (3+ 1) dimensions: multiple soliton solutions, rational solutions and periodic solutions. Computers and Fluids, 86, 357-362.
  • [28] Date, E., Jimbo, M., Kashiwara, M., Miwa, T. 1982. Transformation groups for soliton equations: IV. A new hierarchy of soliton equations of KP-type. Physica D: Nonlinear Phenomena, 4(3), 343-365.
  • [29] Shu-Fang, D. 2008. Soliton solutions for nonisospectral BKP equation. Communications in Theoretical Physics, 49(3), 535.
  • [30] Tuluce Demiray, S., Pandir, Y., Bulut, H. 2014. Generalized Kudryashov method for time-fractional differential equations. In Abstract and applied analysis (Vol. 2014). Hindawi.
  • [31] Akter S, Sen RK, Roshid HO. 2020. Dynamics of interaction between solitary and rogue wave of the space-time fractional Broer–Kaup models arising in shallow water of harbor and coastal zone. SN Appl Sci, 2: 1-12.

(3+1)-Boyutlu B-tipi Kadomtsev-Petviashvili Denkleminin Çözümü için İki Etkili Yöntemin Kullanılması

Yıl 2025, Cilt: 29 Sayı: 1, 54 - 61, 25.04.2025

Mustafa Ekici

https://doi.org/10.19113/sdufenbed.1611725

Öz

Bu çalışma, doğrusal olmayan kısmi diferansiyel denklemler tarafından ortaya konulan karmaşık zorlukların üstesinden gelmek amacıyla iki farklı ve güçlü yöntemi ele almaktadır. Çalışmanın temel amacı, (3+1)-boyutlu B-tipi Kadomtsev-Petviashvili denklemi için yeni ve tam çözümler türetmektir. Araştırmanın odak noktası olarak ele alınan bu denklem, birleşik yöntem ve genelleştirilmiş Kudryashov yöntem kullanılarak dalga çözümleri elde edilerek analiz edilmiştir. Bu yöntemler, doğrusal olmayan sistemlerin teorik analizine katkı sağlarken, çok boyutlu dalga fenomenlerinin daha derinlemesine anlaşılmasını da mümkün kılmaktadır. Türetilen yeni ve tam çözümler, bu denklemlerin fiziksel yorumlarına dair önemli içgörüler sunmakta ve enerji aktarımı, sinyal işleme ve dalga dinamikleri gibi alanlarda ileri düzey uygulamalara zemin hazırlamaktadır. Bu çalışma, kullanılan yöntemlerin etkinliğini vurgulamakta ve doğrusal olmayan fenomenlerin hem teorik hem de pratik düzeyde anlaşılmasını geliştirme potansiyelini ortaya koymaktadır.

Anahtar Kelimeler

The generalized Kudryashov yöntemi B-type Kadomtsev-Petviashvili denklemi Unified yöntem

Kaynakça

  • [1] Sun, Y., Tian, B., Liu, L., 2017. Rogue waves and lump solitons of the (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation for water waves. Commun. Theor. Phys. 68(6), 693.
  • [2] Odibat, Z., and Momani, S. 2008. A generalized differential transform method for linear partial differential equations of fractional order. Applied Mathematics Letters, 21(2), 194-199.
  • [3] Ekici, M., Ayaz, F. 2017. Solution of model equation of completely passive natural convection by improved differential transform method. Research on Engineering Structures and Materials, 3(1), 1-10.
  • [4] El-Sayed, A. M. A., Gaber, M. 2006. The Adomian decomposition method for solving partial differential equations of fractal order in finite domains. Physics Letters A, 359(3), 175-182.
  • [5] El-Sayed, A. M. A., Behiry, S. H., Raslan, W. E. 2010. Adomian's decomposition method for solving an intermediate fractional advection–dispersion equation. Computers & Mathematics with Applications, 59(5), 1759-1765.
  • [6] Kaplan, M., Bekir, A., Akbulut, A. 2016. A generalized Kudryashov method to some nonlinear evolution equations in mathematical physics. Nonlinear Dynamics, 85, 2843-2850.
  • [7] Zhang, S., Tong, J. L., and Wang, W. 2008. A generalized-expansion method for the mKdV equation with variable coefficients. Physics Letters A, 372(13), 2254-2257.
  • [8] Ekici, M., Ünal, M. 2022. Application of the rational (G'/G)-expansion method for solving some coupled and combined wave equations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(1), 116-132.
  • [9] Ünal M., Ekici, M. 2021. The Double (G'/G, 1/G)-Expansion Method and Its Applications for Some Nonlinear Partial Differential Equations. Journal of the Institute of Science and Technology, 11(1), 599-608.
  • [10] Isah, M. A., Yokus, A. 2022. Application of the newly φ^6− model expansion approach to the nonlinear reaction-diffusion equation. Open J. Math. Sci, 6, 269-280.
  • [11] Fan, E. 2000. Extended tanh-function method and its applications to nonlinear equations. Physics Letters A, 277(4), 212-218.
  • [12] Zhang, J. L., Wang, M. L., and Li, X. Z. 2006. The subsidiary ordinary differential equations and the exact solutions of the higher order dispersive nonlinear Schrödinger equation. Physics Letters A, 357(3), 188-195.
  • [13] Wang, M., Li, X., Zhang, J. 2007. Various exact solutions of nonlinear Schrödinger equation with two nonlinear terms. Chaos, Solitons & Fractals, 31(3), 594-601.
  • [14] Ekici M. Exact Solutions of Time-Fractional Thin-Film Ferroelectric Material Equation with Conformable Fractional Derivative. BSJ Eng. Sci. 2025;8(1):179-84.
  • [15] Muhammad, T., Hamoud, A. A., Emadifar, H., Hamasalh, F. K., Azizi, H., Khademi, M. 2022. Traveling wave solutions to the Boussinesq equation via Sardar sub-equation technique. AIMS Mathematics, 7(6), 11134-11149.
  • [16] He, J. H., and Wu, X. H. 2006. Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals, 30(3), 700-708.
  • [17] Ekici, M., Ünal, M. 2020. Application of the exponential rational function method to some fractional soliton equations. In Emerging Applications of Differential Equations and Game Theory (pp. 13-32). IGI Global.
  • [18] Zhang, S., and Zhang, H. Q. 2011. Fractional sub-equation method and its applications to nonlinear fractional PDEs. Physics Letters A, 375(7), 1069-1073.
  • [19] Ekici, M. (2023). Exact solutions to some nonlinear time-fractional evolution equations using the generalized Kudryashov method in mathematical physics. Symmetry, 15(10), 1961.
  • [20] Kadomtsev, B. B., Petviashvili, V. I. (1970). On the stability of solitary waves in weakly dispersing media. In Doklady Akademii Nauk (Vol. 192, No. 4, pp. 753-756). Russian Academy of Sciences.
  • [21] Ablowitz, M. J., Clarkson, P. A. (1991). Solitons, nonlinear evolution equations and inverse scattering (Vol. 149). Cambridge university press.
  • [22] Hirota, R. (2004). The direct method in soliton theory (No. 155). Cambridge University Press.
  • [23] Jimbo, M., Miwa, T. (1983). Solitons and infinite dimensional Lie algebras. Publications of the Research Institute for Mathematical Sciences, 19(3), 943-1001.
  • [24] Dickey, L. A. (2003). Soliton equations and Hamiltonian systems (Vol. 26). World scientific.
  • [25] Takasaki, K., Takebe, T. (1995). Integrable hierarchies and dispersionless limit. Reviews in Mathematical Physics, 7(5), 743-808.
  • [26] Wazwaz, A. M. 2024. Study on a (3+ 1)-dimensional B-type Kadomtsev-Petviashvili equation in nonlinear physics: Multiple soliton solutions, lump solutions, and breather wave solutions. Chaos, Solitons and Fractals, 189, 115668.
  • [27] Wazwaz, A. M. (2013). Two B-type Kadomtsev-Petviashvili equations of (2+ 1) and (3+ 1) dimensions: multiple soliton solutions, rational solutions and periodic solutions. Computers and Fluids, 86, 357-362.
  • [28] Date, E., Jimbo, M., Kashiwara, M., Miwa, T. 1982. Transformation groups for soliton equations: IV. A new hierarchy of soliton equations of KP-type. Physica D: Nonlinear Phenomena, 4(3), 343-365.
  • [29] Shu-Fang, D. 2008. Soliton solutions for nonisospectral BKP equation. Communications in Theoretical Physics, 49(3), 535.
  • [30] Tuluce Demiray, S., Pandir, Y., Bulut, H. 2014. Generalized Kudryashov method for time-fractional differential equations. In Abstract and applied analysis (Vol. 2014). Hindawi.
  • [31] Akter S, Sen RK, Roshid HO. 2020. Dynamics of interaction between solitary and rogue wave of the space-time fractional Broer–Kaup models arising in shallow water of harbor and coastal zone. SN Appl Sci, 2: 1-12.
Toplam 31 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Kısmi Diferansiyel Denklemler, Matematiksel Yöntemler ve Özel Fonksiyonlar, Uygulamalı Matematik (Diğer)
Bölüm Makaleler
Yazarlar

Mustafa Ekici 0000-0003-2494-8229

Yayımlanma Tarihi 25 Nisan 2025
Gönderilme Tarihi 2 Ocak 2025
Kabul Tarihi 19 Şubat 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 29 Sayı: 1

Kaynak Göster

APA Ekici, M. (2025). On solving the (3+1)-dimensional B-type Kadomtsev-Petviashvili equation by using two efficient method. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 29(1), 54-61. https://doi.org/10.19113/sdufenbed.1611725
AMA Ekici M. On solving the (3+1)-dimensional B-type Kadomtsev-Petviashvili equation by using two efficient method. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. Nisan 2025;29(1):54-61. doi:10.19113/sdufenbed.1611725
Chicago Ekici, Mustafa. “On Solving the (3+1)-Dimensional B-Type Kadomtsev-Petviashvili Equation by Using Two Efficient Method”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 29, sy. 1 (Nisan 2025): 54-61. https://doi.org/10.19113/sdufenbed.1611725.
EndNote Ekici M (01 Nisan 2025) On solving the (3+1)-dimensional B-type Kadomtsev-Petviashvili equation by using two efficient method. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 29 1 54–61.
IEEE M. Ekici, “On solving the (3+1)-dimensional B-type Kadomtsev-Petviashvili equation by using two efficient method”, Süleyman Demirel Üniv. Fen Bilim. Enst. Derg., c. 29, sy. 1, ss. 54–61, 2025, doi: 10.19113/sdufenbed.1611725.
ISNAD Ekici, Mustafa. “On Solving the (3+1)-Dimensional B-Type Kadomtsev-Petviashvili Equation by Using Two Efficient Method”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 29/1 (Nisan 2025), 54-61. https://doi.org/10.19113/sdufenbed.1611725.
JAMA Ekici M. On solving the (3+1)-dimensional B-type Kadomtsev-Petviashvili equation by using two efficient method. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 2025;29:54–61.
MLA Ekici, Mustafa. “On Solving the (3+1)-Dimensional B-Type Kadomtsev-Petviashvili Equation by Using Two Efficient Method”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 29, sy. 1, 2025, ss. 54-61, doi:10.19113/sdufenbed.1611725.
Vancouver Ekici M. On solving the (3+1)-dimensional B-type Kadomtsev-Petviashvili equation by using two efficient method. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 2025;29(1):54-61.
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