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Mabrouk, Samah, Rashed, Ahmed, Saleh, Rasha. (1403). Unveiling traveling waves and solitons of dirac integrable system via homogenous balance and singular manifolds methods. سامانه مدیریت نشریات علمی, 13(1), 61-72. doi: 10.22034/cmde.2024.59080.2509
Samah M. Mabrouk; Ahmed S. Rashed; Rasha Saleh. "Unveiling traveling waves and solitons of dirac integrable system via homogenous balance and singular manifolds methods". سامانه مدیریت نشریات علمی, 13, 1, 1403, 61-72. doi: 10.22034/cmde.2024.59080.2509
Mabrouk, Samah, Rashed, Ahmed, Saleh, Rasha. (1403). 'Unveiling traveling waves and solitons of dirac integrable system via homogenous balance and singular manifolds methods', سامانه مدیریت نشریات علمی, 13(1), pp. 61-72. doi: 10.22034/cmde.2024.59080.2509
Mabrouk, Samah, Rashed, Ahmed, Saleh, Rasha. Unveiling traveling waves and solitons of dirac integrable system via homogenous balance and singular manifolds methods. سامانه مدیریت نشریات علمی, 1403; 13(1): 61-72. doi: 10.22034/cmde.2024.59080.2509

Unveiling traveling waves and solitons of dirac integrable system via homogenous balance and singular manifolds methods

Computational Methods for Differential Equations
مقاله 5، دوره 13، شماره 1، فروردین 2025، صفحه 61-72    اصل مقاله (474.12 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.59080.2509
نویسندگان
Samah M. Mabrouk1؛ Ahmed S. Rashed* 2؛ Rasha Saleh1
1Department of Physics and Engineering Mathematics, Faculty of Engineering, Zagazig University, Egypt.
21. Department of Physics and Engineering Mathematics, Faculty of Engineering, Zagazig University, Egypt. 2. Basic Science Department, Faculty of Engineering, Delta University for Science and Technology, Gamasa, 11152, Egypt.
چکیده
This study utilizes two robust methodologies to examine the precise solutions of the Dirac integrable system. The Homogeneous Balance Method (HB) is initially employed to generate an accurate solution. The system of equations for the quasi-solution is solved, where all the equations are of the same nature. The quasi-solution of the traveling wave results in the solitary wave solution of the system. The singular manifold method (SMM) is utilized following the Lie reduction of the Dirac system in order to search for the traveling wave solutions of the system. Both approaches demonstrate the existence of traveling wave solutions inside the system. The precise solutions of the Dirac system are shown in three-dimensional graphs. We have created solutions to the examined problem, including bright solutions, periodic soliton solutions, and complicated solutions.
کلیدواژه‌ها
Dirac integrable system؛ Homogeneous balance method؛ Singular manifold method
مراجع
  • [1]  A. S. Abdel Rady, E. S. Osman, and M. Khalfallah, On soliton solutions for a generalized HHirota-Satsuma coupled KdV equation, Communications in Nonlinear Science and Numerical Simulation, 15(2) (2010), 264-274.
  • [2]  A. S. Abdel Rady and M. Khalfallah, On soliton solutions for Boussinesq-Burgers equations, Communications in Nonlinear Science and Numerical Simulation, 15(4) (2010), 886-894.
  • [3]  G. P. Agrawal, Nonlinear fiber optics, Elsevier Science, 2012.
  • [4]  X. Ai and G. Gui, On the inverse scattering problem and the low regularity solutions for the Dullin-Gottwald-Holm equation, Nonlinear Analysis: Real World Applications, 11(2) (2010), 888-894.
  • [5]  D. Baleanu, M. Inc, A. Yusuf, and A. Isa Aliyu, Optimal system, nonlinear self-adjointness and conservation laws for generalized shallow water wave equation, Open Physics, 16 (2018), 364-370.
  • [6]  D. Baleanu, M. Inc, A. Yusuf, and A. I. Aliyu, Lie symmetry analysis and conservation laws for the time fractional simplified modified Kawahara equation, Open Physics, 16(1) (2018), 302-310.
  • [7]  A. Bekir and A. C. Cevikel, Solitary wave solutions of two nonlinear physical models by tanh-coth method, Communications in Nonlinear Science and Numerical Simulation, 14(5) (2009), 1804-1809.
  • [8]  G. Betchewe, B. B. Thomas, K. K. Victor, and K. T. Crepin, Explicit series solutions to nonlinear evolution equations: The sine-cosine method, Applied Mathematics and Computation, 215(12) (2010), 4239-4247.
  • [9]  A. H. Bhrawy, M. A. Abdelkawy, and A. Biswas, Cnoidal and snoidal wave solutions to coupled nonlinear wave equations by the extended Jacobi’s elliptic function method, Communications in Nonlinear Science and Numerical Simulation, 18(4) (2013), 915-925.
  • [10]  J. Biazar and Z. Ayati, Exp and modified exp function methods for nonlinear Drinfeld-Sokolov system, Journal of King Saud University-Science, 24(4) (2012), 315-318.
  • [11]  R. W. Boyd, Nonlinear optics, Elsevier Science, 2003.
  • [12]  T. F. Chan, E. l. Selim, and M. Nikolova, Algorithms for finding global minimizers of image segmentation and denoising models, SIAM Journal on Applied Mathematics, 66(5) (2006), 1632-1648.
  • [13]  J. M. Conde, P. R. Gordoa, and A. Pickering, A new kind of B¨acklund transformation for partial differential equations, Reports on Mathematical Physics, 70(2) (2012), 149-161.
  • [14]  X. Deng, J. Cao, and X. Li, Travelling wave solutions for the nonlinear dispersion Drinfel’d-Sokolov (D(m,n)) system, Communications in Nonlinear Science and Numerical Simulation, 15(2) (2010), 281-290.
  • [15]  A. Ebaid, An improvement on the exp-function method when balancing the highest order linear and nonlinear terms, Journal of Mathematical Analysis and Applications, 392(1) (2012), 1-5.
  • [16]  L. Edelstein-Keshet, Mathematical models in biology, Society for Industrial and Applied Mathematics Philadelphia, Philadelphia, 2005.
  • [17]  M. K. Elboree, The Jacobi elliptic function method and its application for two component BKP hierarchy equations, Computers & Mathematics with Applications, 62(12) (2011), 4402-4414.
  • [18]  M. Eslami, B. Fathi vajargah, and M. Mirzazadeh, Exact solutions of modified Zakharov-Kuznetsov equation by the homogeneous balance method, Ain Shams Engineering Journal, 5(1) (2014), 221-225.
  • [19]  E. Fan, Two new applications of the homogeneous balance method, Physics Letters A, 265(5) (2000), 353-357.
  • [20]  K. A. Gepreel and A. R. Shehata, Rational Jacobi elliptic solutions for nonlinear differential-difference lattice equations, Applied Mathematics Letters, 25(9) (2012), 1173-1178.
  • [21]  G. Gilboa and S. Osher, Nonlocal operators with applications to image processing, Multiscale Modeling and Simulation, 7(3) (2008), 1005-1028.
  • [22]  G. Hashemi, A novel analytical approximation approach for strongly nonlinear oscillation systems based on the energy balance method and He’s frequency-amplitude formulation, Computational Methods for Differential Equations, 11(3) (2023), 464-477.
  • [23]  O. A. Ilhan, J. Manafian, H. M. Baskonus, and M. Lakestani, Solitary wave solitons to one model in the shallow water waves,The European Physical Journal Plus, 136(3) (2021), 337.
  • [24]  M. Inc, A. Yusuf, A. I. Aliyu, and D. Baleanu, Lie symmetry analysis and explicit solutions for the time fractional generalized Burgers-Huxley equation, Optical and Quantum Electronics, 50(2) (2018), 91-96.
  • [25]  M. Inc, M. Hashemi, and A. Isa Aliyu, Exact solutions and conservation laws of the Bogoyavlenskii equation, Acta Physica Polonica, 133 (2018), 1133-1137.
  • [26]  M. Inc, A. I. Aliyu, A. Yusuf, and D. Baleanu, On the classification of conservation laws and soliton solutions of the long short-wave interaction system, Modern Physics Letters B, 32(18) (2018), 1850202.
  • [27]  A. Isa Aliyu, M. Inc, A. Yusuf, and D. Baleanu, Symmetry analysis, explicit solutions, and conservation laws of a sixth-order nonlinear Ramani equation, Symmetry, 10 (2018), 341.
  • [28]  M. Jafari, A. Zaeim, and S. Mahdion, Scaling symmetry and a new conservation law of the harry dym equation, Mathematics Interdisciplinary Research, 6(2) (2021), 151-158.
  • [29]  M. Jafari, A. Zaeim, and A. Tanhaeivash, Symmetry group analysis and conservation laws of the potential modified KdV equation using the scaling method, International Journal of Geometric Methods in Modern Physics, 19(7) (2022), 2250098.
  • [30]  M. Jafari and R. Darvazebanzade, Approximate symmetry group analysis and similarity reductions of the perturbed mKdV-KS equation, Computational Methods for Differential Equations, 11(1) (2023), 175-182.
  • [31]  M. Jafari and S. Mahdion, Non-classical symmetry and new exact solutions of the kudryashov-sinelshchikov and modified KdV-ZK equations, AUT Journal of Mathematics and Computing, 4(2) (2023), 195-203.
  • [32]  M. Jafari, S. Mahdion, A. Akgül, and S. M. Eldin, New conservation laws of the boussinesq and generalized kadomtsev–petviashvili equations via homotopy operator, Results in Physics, 47 (2023), 106369.
  • [33]  M. Jafari and R. Darvazebanzade, Analyzing of approximate symmetry and new conservation laws of perturbed generalized Benjamin-Bona-Mahony equation, AUT Journal of Mathematics and Computing, 5(1) (2024), 61-69.
  • [34]  B. Kalegowda and R. Raghavachar, Multi-soliton solutions to the generalized boussinesq equation of tenth order, Computational Methods for Differential Equations, 11(4) (2023), 727-737.
  • [35]  M. M. Kassem and A. S. Rashed, Group solution of a time dependent chemical convective process, Applied Mathematics and Computation, 215(5) (2009), 1671-1684.
  • [36]  M. M. Kassem and A. S. Rashed, N-solitons and cuspon waves solutions of (2+1)-dimensional Broer-KaupKupershmidt equations via hidden symmetries of lie optimal system, Chinese Journal of Physics, 57 (2019), 90-104.
  • [37]  M. Khalfallah, Exact traveling wave solutions of the Boussinesq-Burgers equation, Mathematical and Computer Modelling, 49(3) (2009), 666-671.
  • [38]  H. K. Khalil, Nonlinear systems, Prentice Hall, 2002.
  • [39]  K. Khan and M. Ali Akbar, Traveling wave solutions of the (2+1)-dimensional Zoomeron equation and the Burgers equations via the MSE method and the exp-function method, Ain Shams Engineering Journal, 5(1) (2014), 247-256.
  • [40]  S. Kondo and T. Miura,Reaction-diffusion model as a framework for understanding biological pattern formation, Science, 329 (2010), 1616-1620.
  • [41]  M. Lassas, J. L. Mueller, S. Siltanen, and A. Stahel, The Novikov-Veselov equation and the inverse scattering method, part I: Analysis, Physica D: Nonlinear Phenomena, 241(16) (2012), 1322-1335.
  • [42]  B. Lu, Coupling Bäcklund trasnsformation of Riccati equation and division theorem method for traveling wave solutions of some class of NLPDEs, Communications in Nonlinear Science and Numerical Simulation, 17(12) (2012), 4626-4633.
  • [43]  Z. Lü, J. Su, and F. Xie, Construction of exact solutions to the Jimbo-Miwa equation through Bäcklund transformation and symbolic computation, Computers & Mathematics with Applications, 65(4) (2013), 648-656.
  • [44]  W. X. Ma, Multi-component bi-hamiltonian Dirac integrable equations, Chaos, Solitons and Fractals, 39(1) (2009), 282-287.
  • [45]  W. X. Ma and A. Abdeljabbar, A bilinear B¨acklund transformation of a (3+1)-dimensional generalized KP equation, Applied Mathematics Letters, 25(10) (2012), 1500-1504.
  • [46]  W. X. Ma, Y. Zhang, Y. Tang and J. Tu, Hirota bilinear equations with linear subspaces of solutions, Applied Mathematics and Computation 218 (13) (2012), 7174-7183.
  • [47]  S. M. Mabrouk and A. S. Rashed, Analysis of (3 + 1)-dimensional Boiti- Leon-Manna-Pempinelli equation via Lax pair investigation and group transformation method, Computers & Mathematics with Applications, 74(10) (2017), 2546-2556.
  • [48]  S. M. Mabrouk, Chase-repulsion analysis for (2+1)-dimensional Lotka-Volterra system, International Journal of Engineering Research and Technology, 8(6) (2019), 875-879.
  • [49]  B. A. Malomed, Soliton management in periodic systems, Springer New York, New York, 2006.
  • [50]  J. Manafian, L. A. Dawood, and M. Lakestani, New solutions to a generalized fifth-order kdv like equation with prime number p=3 via a generalized bilinear differential operator, Partial Differential Equations in Applied Mathematics, 9 (2024), 100600.
  • [51]  M. Mohamed, S. M. Mabrouk, and A. S. Rashed, Mathematical investigation of the infection dynamics of covid-19 using the fractional differential quadrature method, Computation, 11(10) (2023), 198.
  • [52]  J. D. Murray and S. S. Antman, Mathematical biology. I, an introduction, Springer New York, 2002.
  • [53]  Q. Pang, Study on the behavior of oscillating solitons using the (2+1)-dimensional nonlinear system, Applied Mathematics and Computation, 217(5) (2010), 2015-2023.
  • [54]  K. Parand and J. A. Rad, Exp-function method for some nonlinear PDE’s and a nonlinear ODE’s, Journal of King Saud University-Science, 24(1) (2012), 1-10.
  • [55]  A. Patel and V. Kumar, Dark and kink soliton solutions of the generalized ZK-BBM equation by iterative scheme, Chinese Journal of Physics, 56(3) (2018), 819-829.
  • [56]  A. D. Polyanin and A. I. Zhurov, On RF-pairs, B¨acklund transformations and linearization of nonlinear equations, Communications in Nonlinear Science and Numerical Simulation, 17(2) (2012), 536-544.
  • [57]  A. S. Rashed and M. M. Kassem, Group analysis for natural convection from a vertical plate, Journal of Computational and Applied Mathematics, 222(2) (2008), 392-403.
  • [58]  A. S. Rashed and M. M. Kassem, Hidden symmetries and exact solutions of integro-differential Jaulent-Miodek evolution equation, Applied Mathematics and Computation, 247 (2014), 1141-1155.
  • [59]  A. S. Rashed, Analysis of (3+1)-dimensional unsteady gas flow using optimal system of lie symmetries, Mathematics and Computers in Simulation, 156 (2019), 327-346.
  • [60]  A. S. Rashed, S. M. Mabrouk, and A. M. Wazwaz, Forward scattering for non-linear wave propagation in (3 + 1)-dimensional Kimbo-Miwa equation using singular manifold and group transformation methods, Waves in Random and Complex Media, 32(2) (2022), 663-675.
  • [61]  S. Z. Rida and M. Khalfallah, New periodic wave and soliton solutions for a Kadomtsev-Petviashvili (KP) like equation coupled to a Schr¨odinger equation, Communications in Nonlinear Science and Numerical Simulation, 15(10) (2010), 2818-2827.
  • [62]  R. Saleh, M. Kassem, and S. Mabrouk, Exact solutions of Calgero-Bogoyavlenskii-Schiff equation using the singular manifold method after Lie reductions, Mathematical Methods in the Applied Sciences, 40(16) (2017), 5851-5862.
  • [63]  R. Saleh and A. S. Rashed, New exact solutions of (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation using a combination of Lie symmetry and singular manifold methods, Mathematical Methods in the Applied Sciences, 43(4) (2020), 2045-2055.
  • [64]  H. Sasaki, Inverse scattering problems for the Hartree equation whose interaction potential decays rapidly, Journal of Differential Equations, 252(2) (2012), 2004-2023.
  • [65]  J. J. E. Slotine and W. Li, Applied nonlinear control, Prentice Hall, 1991.
  • [66]  F. Ta¸scan and A. Bekir, Analytic solutions of the (2+1)-dimensional nonlinear evolution equations using the sine-cosine method, Applied Mathematics and Computation, 215(8) (2009), 3134-3139.
  • [67]  Y. Wang and L. Wei, New exact solutions to the (2+1)-dimensional Konopelchenko-Dubrovsky equation, Communications in Nonlinear Science and Numerical Simulation, 15(2) (2010), 216-224.
  • [68]  Y. H. Wang and H. Wang, A coupled kdv system: Consistent tanh expansion, soliton-cnoidal wave solutions and nonlocal symmetries, Chinese Journal of Physics, 56(2) (2018), 598-604.
  • [69]  A. M. Wazwaz, he tanh–coth and the sine-cosine methods for kinks, solitons, and periodic solutions for the Pochhammer-Chree equations, Applied Mathematics and Computation, 195(1) (2008), 24-33.
  • [70]  A. M. Wazwaz, N-soliton solutions for the integrable bidirectional sixth-order Sawada-Kotera equation, Applied Mathematics and Computation, 216(8) (2010), 2317-2320.
  • [71]  A. M. Wazwaz, A study on two extensions of the Bogoyavlenskii-Schieff equation, Communications in Nonlinear Science and Numerical Simulation, 17(4) (2012), 1500-1505.
  • [72]  A. M. Wazwaz, Structures of multiple soliton solutions of the generalized, asymmetric and modified NizhnikNovikov-Veselov equations, Applied Mathematics and Computation, 218(22) (2012), 11344-11349.
  • [73]  L. Wazzan, A modified tanh-coth method for solving the KdV and the KdV-burgers’ equations, Communications in Nonlinear Science and Numerical Simulation, 14(2) (2009), 443-450.
  • [74]  L. Wazzan, A modified tanh-coth method for solving the general Burgers-Fisher and the Kuramoto-Sivashinsky equations, Communications in Nonlinear Science and Numerical Simulation, 14(6) (2009), 2642-2652.
  • [75]  B. Wei, C. Hu, X. Guan, Z. Luan, M. Yao, and W. Liu, Analytic study on soliton solutions for a dirac integrable equation, Optik - International Journal for Light and Electron Optics, 183 (2019), 869-874.
  • [76]  X. X. Xu and Y. P. Sun, An integrable coupling hierarchy of Dirac integrable hierarchy, its liouville integrability and Darboux transformation, The Journal of Nonlinear Sciences and Applications, 10(6) (2017), 3328-3343.
  • [77]  M. Yaghobi Moghaddam, A. Asgari, and H. Yazdani, Exact travelling wave solutions for the generalized nonlinear Schr¨odinger (GNLS) equation with a source by extended tanh-coth, sine-cosine and exp-function methods, Applied Mathematics and Computation, 210(2) (2009), 422-435.
  • [78]  Y. Ye, Z. Li, C. Li, S. Shen, and W. X. Ma, A generalized Dirac soliton hierarchy and its bi-hamiltonian structure, Applied Mathematics Letters, 60 (2016), 67-72.
  • [79]  M. X. Yu, B. Tian, Y. Q. Yuan, Y. Sun, and X. X. Du, Conservation laws, solitons, breather and rogue waves for the (2+1)-dimensional variable-coefficient Nizhnik-Novikov-Veselov system in an inhomogeneous medium, Chinese Journal of Physics, 56(2) (2018), 645-658.
  • [80]  E. M. Zayed and M. A. Abdelaziz, Exact solutions for the nonlinear schr¨odinger equation with variable coefficients using the generalized extended tanh-function, the sine-cosine and the exp-function methods, Applied Mathematics and Computation, 218(5) (2011), 2259-2268.
  • [81]  J. L. Zhang, Y. M. Wang, M. L. Wang, and Z. D. Fang, New applications of the homogeneous balance principle, Chinese Physics, 12(3) (2003), 245-250.
  • [82]  J. Zhang, Y. Zhao, F. You, and Z. Popowicz, A new super extension of Dirac hierarchy, Abstract and Applied Analysis, 2014 (2014), 472101.
  • [83]  Y. Zhou, F. Yang, and Q. Liu, Reduction of the Sharma-Tasso-Olver equation and series solutions, Communications in Nonlinear Science and Numerical Simulation, 16(2) (2011), 641-646.
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