دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات45
تعداد شماره‌ها1,360
تعداد مقالات16,664
تعداد مشاهده مقاله53,905,952
تعداد دریافت فایل اصل مقاله16,527,266
Khalique, Chaudry, Adeyemo, Oke, Gaxela, Yanga. (1403). On the dynamics of newly generated analytical solutions and conserved vectors of a generalized 3D KP-BBM equation. سامانه مدیریت نشریات علمی, 13(2), 682-708. doi: 10.22034/cmde.2024.60476.2589
Chaudry Masood Khalique; Oke Davies Adeyemo; Yanga Gaxela. "On the dynamics of newly generated analytical solutions and conserved vectors of a generalized 3D KP-BBM equation". سامانه مدیریت نشریات علمی, 13, 2, 1403, 682-708. doi: 10.22034/cmde.2024.60476.2589
Khalique, Chaudry, Adeyemo, Oke, Gaxela, Yanga. (1403). 'On the dynamics of newly generated analytical solutions and conserved vectors of a generalized 3D KP-BBM equation', سامانه مدیریت نشریات علمی, 13(2), pp. 682-708. doi: 10.22034/cmde.2024.60476.2589
Khalique, Chaudry, Adeyemo, Oke, Gaxela, Yanga. On the dynamics of newly generated analytical solutions and conserved vectors of a generalized 3D KP-BBM equation. سامانه مدیریت نشریات علمی, 1403; 13(2): 682-708. doi: 10.22034/cmde.2024.60476.2589

On the dynamics of newly generated analytical solutions and conserved vectors of a generalized 3D KP-BBM equation

Computational Methods for Differential Equations
مقاله 24، دوره 13، شماره 2، خرداد 2025، صفحه 682-708    اصل مقاله (2.85 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.60476.2589
نویسندگان
Chaudry Masood Khalique* 1؛ Oke Davies Adeyemo2؛ Yanga Gaxela2
1Material Science, Innovation and Modelling Research Focus Area, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, Republic of South Africa.
2Material Science, Innovation and Modelling Research Focus Area, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, Republic of South Africa.
چکیده
This paper examines a high-dimensional non-linear partial differential equation called the generalized Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation exists in three dimensions. The Lie symmetry analysis of the equation is carried out step-by-step. As a result, we found symmetries from which various group-invariant solutions arise, leading to numerous solutions of interest that satisfy the KP-BBM equation. Secured solutions of interest include hyperbolic functions and elliptic functions, with the latter being the more general of the two solutions. Additionally, a significant number of algebraic solutions with arbitrary functions are also obtained. Furthermore, the dynamics of the solutions are further explored diagrammatically using computer software. In the concluding section, various conservation laws of the underlying model are derived via the multiplier method and the Noether theorem. 
کلیدواژه‌ها
A generalized three-dimensional KP-BBM equation؛ Lie symmetry analysis؛ Group-invariant and analytical solutions؛ Conservation laws
مراجع
  • [1] M. A. Abdou, Exact periodic wave solutions to some nonlinear evolution equations, Int. J. Nonlinear Sci., 6 (2008), 145–153.
  • [2] M. J. Ablowitz and P. A. Clarkson, Nonlinear Evolution Equations and Inverse Scattering, Solitons, Cambridge University Press, Cambridge, UK, 1991.
  • [3] O. D. Adeyemo, C. M. Khalique, Y. S. Gasimov, and F. Villecco, Variational and non-variational approaches with Lie algebra of a generalized (3+1)-dimensional nonlinear potential Yu-Toda-Sasa-Fukuyama equation in Engineering and Physics, Alex. Eng. J., 63 (2023), 17–43.
  • [4] O. D. Adeyemo, L. Zhang, and C. M. Khalique, Bifurcation theory, Lie group-invariant solutions of subalgebras and conservation laws of a generalized (2+1)-dimensional BK equation Type II in plasma physics and fluid mechanics, Mathematics, 10 (2022), 2391.
  • [5] O. D. Adeyemo, L. Zhang, and C. M. Khalique, Optimal solutions of Lie subalgebra, dynamical system, travelling wave solutions and conserved currents of (3+1)-dimensional generalized ZakharovKuznetsov equation type I, Eur. Phys. J. Plus, 137 (2022), 954.
  • [6] O. D. Adeyemo and C. M. Khalique, An optimal system of Lie subalgebras and group-invariant solutions with conserved currents of a (3+1)-D fifth-order nonlinear model with applications in electrical electronics, chemical engineering and pharmacy, J. Nonlinear Math. Phys., 30 (2023), 843–916.
  • [7] O. D. Adeyemo, T. Motsepa, and C. M. Khalique, A study of the generalized nonlinear advection-diffusion equation arising in engineering sciences, Alex. Eng. J., 61 (2022), 185–194.
  • [8] O. D. Adeyemo, Applications of cnoidal and snoidal wave solutions via an optimal system of subalgebras for a generalized extended (2+1)-D quantum Zakharov-Kuznetsov equation with power-law nonlinearity in oceanography and ocean engineering, J. Ocean Eng. Sci., 9 (2024), 126–153.
  • [9] A. S. Alhasanat, On the minimal speed determinacy of traveling waves to a three-species competition model, Adv. Math. Models Appl., 8 (2023), 34–44.
  • [10] U. Al Khawajaa, H. Eleuchb, and H. Bahloulid, Analytical analysis of soliton propagation in microcavity wires, Results Phys., 12 (2019), 471–474.
  • [11] B. Babajanov and F. Abdikarimov, Expansion method for the loaded modified Zakharov-Kuznetsov equation, Adv. Math. Models Appl., 7 (2022), 168–177.
  • [12] Y. Chen and Z Yan, New exact solutions of (2+1)-dimensional Gardner equation via the new sine-Gordon equation expansion method, Chaos Solitons Fract., 26 (2005), 399–406.
  • [13] S. S. Chen, B. Tian, J. Chai, X. Y. Wu, and Z. Du, Lax pair, Lax pair binary Darboux transformations and dark-soliton interaction of a fifth-order defocusing nonlinear Schr¨odinger equation for the attosecond pulses in the optical fiber communication, Wave Random Complex, 30 (2020), 389–402.
  • [14] C. Chun and R. Sakthivel, Homotopy perturbation technique for solving two point boundary value problemscomparison with other methods, Comput. Phys. Commun., 181 (2010), 1021–1024.
  • [15] M. T. Darvishi and M. Najafi, A modification of extended homoclinic test approach to solve the (3+1)-dimensional potential-YTSF equation, Chin. Phys. Lett., 28 (2011), 040202.
  • [16] S.T. Demiray and S. Duman, MTEM to the (2+1)-dimensional ZK equation and Chafee-Infante equation, Adv. Math. Models Appl., 6 (2021), 63–70.
  • [17] X. X. Du, B. Tian, Q. X. Qu, Y. Q. Yuan, and X. H. Zhao, Lie group analysis, solitons, self-adjointness and conservation laws of the modified Zakharov-Kuznetsov equation in an electron-positron-ion magnetoplasma, Chaos Solitons Fract., 134 (2020), 109709.
  • [18] A.S. Farajov, On a solvability of the nonlinear inverse boundary value problem for the Boussinesq equation, Adv. Math. Models Appl., 7 (2022), 241–248.
  • [19] X. Y. Gao, Y. J. Guo, and W. R. Shan, Shallow water in an open sea or a wide channel: Auto- and non-autoB¨acklund transformations with solitons for a generalized (2+1)-dimensional dispersive long-wave system, Chaos Solit. Fractals, 138 (2020), 109950.
  • [20] X. Y. Gao, Y. J. Guo, and W. R. Shan, Water-wave symbolic computation for the Earth, Enceladus and Titan: The higher-order Boussinesq-Burgers system, auto-and non-auto-Bcklund transformations, Appl. Math. Lett., 104 (2020), 106170.
  • [21] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 7th Edition, Academic Press, New York, 2007.
  • [22] C. H. Gu, Soliton Theory and Its Application, Zhejiang Science and Technology Press, Zhejiang, China, 1990.
  • [23] J. H. He and X. H. Wu, Exp-function method for nonlinear wave equations, Chaos Solitons Fract., 30 (2006), 700–708.
  • [24] M. F. Hoque, H. O. Roshid, and F. S. Alshammari, Higher-order rogue wave solutions of the Kadomtsev Petviashvili-Benjanim Bona Mahony (KP-BBM) model via the Hirota bilinear approach, Phys. Scr., 95 (2020), 115215.
  • [25] R. Hirota, The Direct Method in Soliton Theory, Cambridge University Press, Cambridge, UK, 2004.
  • [26] 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.
  • [27] C. M. Khalique and O. D. Adeyemo, A study of (3+1)-dimensional generalized Korteweg-de Vries-ZakharovKuznetsov equation via Lie symmetry approach, Results Phys., 18 (2020), 103197.
  • [28] C. M. Khalique and O. D. Adeyemo, Closed-form solutions and conserved vectors of a generalized (3+1)dimensional breaking soliton equation of engineering and nonlinear science, Mathematics, 8 (2020), 1692.
  • [29] N. A. Kudryashov and N. B. Loguinova, Extended simplest equation method for nonlinear differential equations, Appl. Math. Comput., 205 (2008), 396-402.
  • [30] N. A. Kudryashov, Simplest equation method to look for exact solutions of nonlinear differential equations, Chaos Solitons Fract., 24 (2005), 1217–1231
  • [31] S. Liu, Multiple rogue wave solutions for the (3+1)-dimensional generalized Kadomtsev-Petviashvili BenjaminBona-Mahony equation, Chinese. J. Phys., 68 (2020), 961–970.
  • [32] V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons, Springer, New York, USA, 1991.
  • [33] A. Mekki and M. M. Ali, Numerical simulation of Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equations using finite difference method, Appl. Math. Comput., 219 (2013), 11214–11222.
  • [34] I. E. Mhlanga and C. M. Khalique, A study of a generalized Benney–Luke equation with time-dependent coefficients, Nonlinear Dyn., 90 (2017), 1535–1544.
  • [35] E. Noether, Invariante variations probleme, Nachr. d. K¨onig. Gesellsch. d. Wiss. zu G¨ottingen, Math-phys. Klasse, 2 (1918), 235–257.
  • [36] P. J. Olver, Applications of Lie Groups to Differential Equations, second ed., Springer-Verlag, Berlin, Germany, 1993.
  • [37] M. S. Osman, One-soliton shaping and inelastic collision between double solitons in the fifth-order variablecoefficient Sawada-Kotera equation, Nonlinear Dynam., 96 (2019), 1491–1496.
  • [38] L. V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, USA, 1982.
  • [39] A. H. Salas and C. A. Gomez, Application of the Cole-Hopf transformation for finding exact solutions to several forms of the seventh-order KdV equation, Math. Probl. Eng., 2010.
  • [40] M. Song, C. X. Yang, B. and G. Zhang, Exact solitary wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equation, Appl. Math. Comput., 217 (2010), 1334–1339.
  • [41] S. Q. Tang, X. L. Huang, and W. T. Huang, Bifurcations of travelling wave solutions for the generalized KP-BBM equation, Appl. Math. Comput., 216 (2010), 2881–2890.
  • [42] K. U. H. Tariq and A. R. Seadawy, Soliton solutions of (3+1)-dimensional Korteweg-de Vries Benjamin-BonaMahony, Kadomtsev-Petviashvili Benjamin-Bona-Mahony and modified Korteweg de Vries-Zakharov-Kuznetsov equations and their applications in water waves, J. King. Saud. Univ. Sci., 31 (2019), 8–13.
  • [43] M. Wang, X. Li, and J. Zhang, The (G0/G)− expansion method and travelling wave solutions for linear evolution equations in mathematical physics, Phys. Lett. A, 24 (2005), 1257–1268.
  • [44] A. M. Wazwaz, Exact soliton and kink solutions for new (3+1)-dimensional nonlinear modified equations of wave propagation, Open Eng., 7 (2017), 169–174.
  • [45] A. M. Wazwaz, Exact solutions of compact and noncompact structures for the KP-BBM equation, Nonlinear. Dyn., 169 (2005), 700–712.
  • [46] A. M. Wazwaz, Partial Differential Equations, CRC Press, Boca Raton, Florida, USA, 2002.
  • [47] A. M. Wazwaz, The tanh and sine-cosine method for compact and noncompact solutions of nonlinear Klein Gordon equation, Appl. Math. Comput., 167 (2005) 1179–1195.
  • [48] A. M. Wazwaz, The tanh method for generalized forms of nonlinear heat conduction and Burgers-Fisher equations, Appl. Math. Comput., 169 (2005), 321–338.
  • [49] A. M. Wazwaz, Traveling wave solution to (2+1)-dimensional nonlinear evolution equations, J. Nat. Sci. Math., 1 (2007), 1–13.
  • [50] J. Weiss, M. Tabor, and G. Carnevale, The Painl´ev´e property and a partial differential equations with an essential singularity, Phys. Lett. A, 109 (1985), 205–208.
  • [51] Y. Xie and L. Li. Multiple-order breathers for a generalized (3+1)-dimensional Kadomtsev-Petviashvili BenjaminBona-Mahony equation near the offshore structure, Math. Comput. Simul., 193 (2022), 19–31.
  • [52] Y. Yin, B. Tian, X.Y. Wu, H.M. Yin, Ch. R. Zhang, Lump waves and breather waves for a (3+1)-dimensional generalized Kadomtsev-Petviashvili Benjamin-Bona-Mahony equation for an offshore structure, Mod. Phys. Lett. B., 32 (2018), 1850031.
  • [53] X. Zeng and D. S. Wang, A generalized extended rational expansion method and its application to (1+1)dimensional dispersive long wave equation, Appl. Math. Comput., 212 (2009), 296–304.
  • [54] L. Zhang and C. M. Khalique, Classification and bifurcation of a class of second-order ODEs and its application to nonlinear PDEs, Discrete Contin. Dyn. Syst. - S., 11 (2018), 777–790.
  • [55] C. R. Zhang, B. Tian, Q. X. Qu, L. Liu, and H. Y. Tian, Vector bright solitons and their interactions of the couple FokasLenells system in a birefringent optical fiber, Z. Angew. Math. Phys., 71 (2020), 1–19.
  • [56] Y. Zhou, M. Wang, and Y. Wang, Periodic wave solutions to a coupled KdV equations with variable coefficients, Phys. Lett. A, 308 (2003), 31–36.
 

آمار
تعداد مشاهده مقاله: 155
تعداد دریافت فایل اصل مقاله: 420


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب