Nội dung được dịch bởi AI, chỉ mang tính chất tham khảo
Giải pháp chính xác của phương trình Kadomtsev–Petviashvili (3+1)-chiều gia hạn phân thời gian
Springer Science and Business Media LLC - Trang 1-16 - 2024
Tóm tắt
Phương trình Kadomtsev–Petviashvili (3+1)-chiều gia hạn được sử dụng phổ biến trong các lĩnh vực như cơ học chất lỏng, quang học, và nhiều lĩnh vực khác. Trong bài báo này, chúng tôi đưa ra một phương trình Kadomtsev–Petviashvili (3+1)-chiều phân thời gian mới dựa trên đạo hàm phân dạng có thể kiểm soát lần đầu tiên. Với sự trợ giúp của phương pháp bilinear Hirota, chúng tôi thu được các nghiệm N-soliton, breather và lump của phương trình Kadomtsev–Petviashvili (3+1)-chiều phân thời gian. Ngoài ra, phương pháp biến tần số nửa và phương pháp mở rộng $$exp(\phi (-\xi ))$$ -expansion được giới thiệu để tạo ra các nghiệm chính xác của phương trình này. Bằng cách chọn các tham số phù hợp, các nghiệm này có thể giúp giải quyết các vấn đề trong khoa học biển, lý thuyết dao động và nhiều lĩnh vực khác được trình bày qua đồ họa 3D, biểu đồ đường viền và biểu đồ mật độ. Các phát hiện của công trình này có thể mở rộng hơn nữa nghiên cứu về các phương trình vi phân riêng phần phân frac.
Từ khóa
#Kadomtsev–Petviashvili equation #time-fractional #Hirota bilinear method #soliton solutions #marine scienceTài liệu tham khảo
Wang, K.L.: Exact travelling wave solution for the local fractional Camassa-Holm-Kadomtsev-Petviashvili equation. Alex. Eng. J. 63, 371–376 (2023)
Kaur, L., Wazwaz, A.-M.: Dynamical analysis of soliton solutions for space-time fractional Calogero-Degasperis and Sharma-Tasso-Olver equations. Rom. Rep. Phys. 74, 108 (2022)
Saini, S., Kumar, R., Arora, R., Kumar, K., et al.: Symmetry analysis and wave solutions of the fisher equation using conformal fractional derivatives. J. Appl. Math. (2023). https://doi.org/10.1155/2023/1633450
Yaslan, H.: Legendre collocation method for the nonlinear space-time fractional partial differential equations. Iran. J. Sci. Technol. Trans. A Sci. 44, 239–249 (2020)
Khristenko, U., Wohlmuth, B.: Solving time-fractional differential equations via rational approximation. IMA J. Numer. Anal. 43(3), 1263–1290 (2023)
Obeidat, N.A., Bentil, D.E.: Convergence analysis of the fractional decomposition method with applications to time-fractional biological population models. Num. Methods Part. Differ. Equ. 39(1), 696–715 (2023)
Alam, M.N., Akash, H.S., Saha, U., Hasan, M.S., Parvin, M.W., Tunç, C.: Bifurcation analysis and solitary wave analysis of the nonlinear fractional soliton neuron model. Iran. J. Sci. (2023). https://doi.org/10.1007/s40995-023-01555-y
Agarwal, R.P., Gala, S., Ragusa, M.A.: A regularity criterion in weak spaces to Boussinesq equations. Mathematics 8(6), 920 (2020)
Gala, S., Ragusa, M.A.: A logarithmic regularity criterion for the two-dimensional MHD equations. J. Math. Anal. Appl. 444(2), 1752–1758 (2016)
Wang, K.: New perspective to the fractal Konopelchenko–Dubrovsky equations with M-truncated fractional derivative. Int. J. Geom. Methods Mod. Phys. 20(05), 2350072 (2023)
Hamid, M., Usman, M., Zubair, T., Haq, R.U., Shafee, A.: An efficient analysis for N-soliton, lump and lump-kink solutions of time-fractional (2+1)-Kadomtsev–Petviashvili equation. Phys. A Stat. Mech. Appl. 528, 121320 (2019)
Khalil, R., Horani, A.: Mohammed and Yousef, Abdelrahman and Sababheh, Mohammad, a new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)
Abdeljawad, T.: On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015)
Biswas, S., Ghosh, U., Raut, S.: Construction of fractional granular model and bright, dark, lump, breather types soliton solutions using Hirota bilinear method. Chaos, Solitons Fractals 172, 113520 (2023)
Gupta, R.K.: Bifurcation analysis, chaotic analysis and diverse optical soliton solutions of time-fractional (2+1) dimensional generalized Camassa-Holm Kadomtsev-Petviashvili equation arising in shallow water waves. Phys. Scr. 98(12), 125241 (2023)
Ullah, M.S.: Interaction solution to the (3+1)-dimension negative-order KdV first structure. Part. Differ. Equ. Appl. Math. 8, 100566 (2023)
Younis, M., Zafar, A.: Exact solution to nonlinear differential equations of fractional order via (G’/G)-expansion method. Appl. Math. 5(1), 1 (2014)
Guner, O., Atik, H., Kayyrzhanovich, A.A.: New exact solution for space-time fractional differential equations via (G’/G)-expansion method. Optik 130, 696–701 (2017)
Alam, M.N., Islam, S.R.: The agreement between novel exact and numerical solutions of nonlinear models. Part. Differ. Equ. Appl. Math. 8, 100584 (2023)
Nur, A.M.: Soliton solutions to the electric signals in telegraph lines on the basis of the tunnel diode. Part. Differ. Equ. Appl. Math. 7, 100491 (2023)
Nur, A.M.: An analytical technique to obtain traveling wave solutions to nonlinear models of fractional order. Part. Differ. Equ. Appl. Math. 8, 100533 (2023)
Nur, A.M., Islam, S., İlhan, O.A., Bulut, H.: Some new results of nonlinear model arising in incompressible Visco-elastic Kelvin-Voigt fluid. Math. Methods Appl. Sci. 45(16), 10347–10362 (2022)
Saha Ray, S.: New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods. Chin. Phys. B 25(4), 040204 (2016)
Murad, M.A.S., Hamasalh, F.K., Ismael, H.F.: Optical soliton solutions for time-fractional Fokas system in optical fiber by new Kudryashov approach. Optik 280, 170784 (2023)
Nur, A.M., Ilhan, O.A., Manafian, J., Asjad, M.I., Rezazadeh, H., Baskonus, H.M., Macias-Diaz, J.E.: New results of some of the conformable models arising in dynamical systems. Adv. Math. Phys. 1–13, 2022 (2022)
Zhou, Q., Mirzazadeh, M., Zerrad, E., Biswas, A., Belic, M.: Bright, dark, and singular solitons in optical fibers with Spatio-temporal dispersion and spatially dependent coefficients. J. Mod. Opt. 63(10), 950–954 (2016)
Guner, O., Bekir, A.: The Exp-function method for solving nonlinear space-time fractional differential equations in mathematical physics. J. Assoc. Arab Univ. Basic Appl. Sci. 24, 277–282 (2017)
Ananna, S.N., Tianqing An, Md., Asaduzzaman, Md., Rana, M.S., et al.: Sine-Gordon expansion method to construct the solitary wave solutions of a family of 3D fractional WBBM equations. Results Phys. 40, 105845 (2022)
Ahmadinia, M., Safari, Z.: Analysis of local discontinuous Galerkin method for time-space fractional sine-Gordon equations. Appl. Numer. Math. 148, 1–17 (2020)
Bashar, M.H., Tahseen, T., Nur Hasan, S.H.A.H.E.N.: Application of the advanced exp (-\(\varphi \) (\(\xi \)))-expansion method to the nonlinear conformable time-fractional partial differential equations. Turk. J. Math. Comput. Sci. 13(1), 68–80 (2021)
Asghari, Y., Eslami, M., Rezazadeh, H.: Soliton solutions for the time-fractional nonlinear differential-difference equation with conformable derivatives in the ferroelectric materials. Opt. Quant. Electron. 55(4), 289 (2023)
Gómez, C.A., Salas, A.H.: The variational iteration method combined with improved generalized tanh-coth method applied to Sawada-Kotera equation. Appl. Math. Comput. 217(4), 1408–1414 (2010)
Manafian, J., Lakestani, M.: A new analytical approach to solve some of the fractional-order partial differential equations. Indian J. Phys. 91, 243–258 (2017)
Seadawy, A.R., Manafian, J.: New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod. Results Phys. 8, 1158–1167 (2018)
Mohammed, W.W., Qahiti, R., Ahmad, H., Baili, J., Mansour, F.E., El-Morshedy, M.: Exact solutions for the system of stochastic equations for the ion sound and Langmuir waves. Results Phys. 30, 104841 (2021)
Shahen, N.H.M., Ali, M.S., Rahman, M.M., et al.: Interaction among lump, periodic, and kink solutions with dynamical analysis to the conformable time-fractional Phi-four equation. Part. Differ. Equ. Appl. Math. 4, 100038 (2021)
Wang, K.-J., Peng, X., Shi, F.: Nonlinear Dynamic Behaviors Of The Fractional (3+1)-Dimensional Modified Zakharov-Kuznetsov Equation. Fractals 31(07), 2350088 (2023)
Wazwaz, A.-M.: Painlevé integrability and lump solutions for two extended (3+1)-and (2+1)-dimensional Kadomtsev-Petviashvili equations. Nonlinear Dyn. 111(4), 3623–3632 (2023)
Shen, Y., Tian, B., Cheng, C.-D., Zhou, T.-Y.: N-soliton, M th-order breather, H th-order lump, and hybrid solutions of an extended (3+1)-dimensional Kadomtsev-Petviashvili equation. Nonlinear Dyn. 111(11), 10407–10424 (2023)
Rezazadeh, H., et al.: New exact solutions of nonlinear conformable time-fractional Phi-4 equation. Chin. J. Phys. 56(6), 2805–2816 (2018)
Gupta, R.K., Yadav, P.: Optical solitons and exact solutions of the (2+1) dimensional conformal time fractional Kundu-Mukherjee-Naskar equation via novel extended techniques. Phys. Scr. 98(6), 065015 (2023)
Sherriffe, D., Behera, D.: Analytical approach for travelling wave solution of non-linear fifth-order time-fractional Korteweg-De Vries equation. Pramana 96(2), 64 (2022)
Atangana, A., Baleanu, D., Alsaedi, A.: New properties of conformable derivative. Open Math. 13(1), 000010151520150081 (2015)
Ghanbari, B., Baleanu, D.: New optical solutions of the fractional Gerdjikov-Ivanov equation with conformable derivative. Front. Phys. 8, 167 (2020)
Biswas, S., Ghosh, U.: Formation and shock solutions of the time fractional (2+ 1) and (3+ 1)-Dimensional Boiti-Leon-Manna-Pempinelli equations. Int. J. Appl. Comput. Math. 9(3), 20 (2023)
He, J.-H.: Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics. Int. J. Turbo Jet Eng. 14(1), 23–28 (1997)
Wang, K.-J., Shi, F., Wang, G.-D.: Periodic wave structure of the fractal generalized fourth-order Boussinesq equation traveling along the non-smooth boundary. Fractals 30(09), 2250168 (2022)
Wang, K.J., Shi, F., Wang, G.D.: Abundant soliton structures to the (2+1)-dimensional Heisenberg ferromagnetic spin chain dynamical model. Adv. Math. Phys. (2023). https://doi.org/10.1155/2023/4348758
He, J.-H.: Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B 20(10), 1141–1199 (2006)