Solitary waves with two new nonlocal boussinesq types equations using a couple of integration schemes

Samir, Islam; Arnous, Ahmed H.; Elsherbeny, Ahmed M.; Mirzazadeh, Mohammad; Hashemi, Mir Sajjad; Eslami, Mostafa

doi:10.22034/cmde.2024.57112.2390

فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری

تعداد نشریات	45
تعداد شماره‌ها	1,398
تعداد مقالات	17,070
تعداد مشاهده مقاله	55,095,939
تعداد دریافت فایل اصل مقاله	17,518,414

	Solitary waves with two new nonlocal boussinesq types equations using a couple of integration schemes
Computational Methods for Differential Equations
مقاله 9، دوره 12، شماره 4، دی 2024، صفحه 749-762 اصل مقاله (4.33 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.57112.2390
نویسندگان
Islam Samir¹؛ Ahmed H. Arnous²؛ Ahmed M. Elsherbeny¹؛ Mohammad Mirzazadeh^* ³؛ Mir Sajjad Hashemi⁴؛ Mostafa Eslami^* ⁵
¹Department of Physics and Mathematics Engineering, Faculty of Engineering, Ain Shams University-11517, Cairo, Egypt.
²Ain Shams University-11517, Cairo, Egypt.
³Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran.
⁴Department of Computer Engineering, Biruni University, 34010 Istanbul, Turkey.
⁵Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
چکیده
The Boussinesq equation and its related types are able to provide a significant explanation for a variety of different physical processes that are relevant to plasma physics, ocean engineering, and fluid flow. Within the framework of shallow water waves, the aim of this research is to find solutions for solitary waves using newly developed nonlocal models of Boussinesq’s equations. The extraction of bright and dark solitary wave solutions along with bright–dark hybrid solitary wave solutions is accomplished through the implementation of two integration algorithms. The general projective Riccati equations method and the enhanced Kudryashov technique are the ones that have been implemented as techniques. The enhanced Kudryashov method combines the benefits of both the original Kudryashov method and the newly developed Kudryashov method, which may generate bright, dark, and singular solitons. The Projective Riccati structure is determined by two functions that provide distinct types of hybrid solitons. The solutions get increasingly diverse as these functions are combined. The techniques that were applied are straightforward and efficient enough to provide an approximation of the solutions discovered in the research. Furthermore, these techniques can be utilized to solve various kinds of nonlinear partial differential equations in mathematical physics and engineering. In addition, plots of the selected solutions in three dimensions, two dimensions, and contour form are provided.
کلیدواژه‌ها
Nonlocal؛ Boussinesq؛ Water waves؛ Kudryashov؛ Riccati

مراجع
[1] G. Akram, M. Sadaf, S. Arshed, and Fizza Sameen, Bright, dark, kink, singular and periodic soliton solutions of Lakshmanan{Porsezian{Daniel model by generalized projective Riccati equations method, Optik, 241 (2021), 167051. [2] A. H. Arnous, M. Ekici, S. P. Moshokoa, M. Zaka Ullah, A. Biswas, and M. Belic. Solitons in Nonlinear Directional Couplers with Optical Metamaterials by Trial Function Scheme. Acta Physica Polonica A, 132(4) (2017), 1399-1410. [3] A. H. Arnous, Optical solitons with Biswas{Milovic equation in magneto-optic waveguide having Kudryashov’s law of refractive index, Optik, 247 (2021), 167987. [4] A. H. Arnous, Q. Zhou, A. Biswas, P. Guggilla, S. Khan, Y. Yldrm, A. S. Alshomrani, and H. M. Alshehri, Optical solitons in ber Bragg gratings with cubic-quartic dispersive reectivity by enhanced Kudryashov’s approach, Physics Letters A, 422 (2022), 127797. [5] A. H. Arnous, A. Biswas, Y. Yldrm, Q. Zhou, W. Liu, A. S. Alshomrani, and H. M. Alshehri, Cubic quartic optical soliton perturbation with complex Ginzburg Landau equation by the enhanced Kudryashov’s method, Chaos, Solitons & Fractals, 155 (2022), 111748. [6] J. V. Bolussinesq, Theorie des ondes et des remous qui se propagent le long dun canal rectangulaire horizontal, en communiquant au liquide contene dans ce canal des vitesses sensiblement pareilles de la surface au fond, J. Math. Pures Appl, 17(9) (1872), 55-108. [7] Y. M. Chu, M. Inc, M. S. Hashemi, and S. Eshaghi, Analytical treatment of regularized Prabhakar fractional dierential equations by invariant subspaces, Computational and Applied Mathematics, 41(6) (2022), 271. [8] M. T. Darvishi, M. Naja, and A. M. Wazwaz, Soliton solutions for Boussinesq-like equations with spatio-temporal dispersion, Ocean Eng, 130 (2017), 228-240. [9] M. M. A. El-Sheikh, A. R. Seadawy, H. M. Ahmed, A. H. Arnous, and W. B. Rabie, Dispersive and propagation of shallow water waves as a higher order nonlinear Boussinesq-like dynamical wave equations, Physica A: Statistical Mechanics and its Applications, 537 (2020), 122662. [10] M. S. Hashemi, A novel approach to nd exact solutions of fractional evolution equations with non-singular kernel derivative, Chaos, Solitons & Fractals, 152 (2021), 111367. [11] R. S. Johnson, A modern introduction to the mathematical theory of water waves. Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 1997. [12] N. A. Kudryashov, One method for nding exact solutions of nonlinear dierential equations, Communications in Nonlinear Science and Numerical Simulation, 17(6) (2012), 2248-2253. [13] N. A. Kudryashov, Method for nding highly dispersive optical solitons of nonlinear dierential equations, Optik, 206 (2020), 163550. [14] B-Q. Li, A. M. Wazwaz, and Y. L. Ma, Two new types of nonlocal Boussinesq equations in water waves: Bright and dark soliton solutions, Chinese Journal of Physics, 77 (2022), 1782-1788. [15] B. Li and Y. Chen, Nonlinear Partial Dierential Equations Solved by Projective Riccati Equations Ansatz, Z. Naturforsch, 58(a) (2003), 511-519. [16] P. A. Madsen, H. B. Bingham, H. Liu, A new Boussinesq method for fully nonlinear waves from shallow to deep water, J. Fluid Mech., 462 (2002), 1-30. [17] W. X. Ma and J. S. He, A second Wronskian formulation of the Boussinesq equation, Nonlinear Anal, 70 (2009), 4245-4258. [18] Y. L. Ma and B-Q. Li, Bifurcation solitons and breathers for the nonlocal Boussinesq equations, Appl. Math. Lett, 124 (2022), 107677. [19] V. G. Makhankov, Dynamics of classical solitons (in nonintegrable systems), Phys. Rep., 35 (1978), 1-28. [20] T. Mathanaranjan, An eective technique for the conformable space-time fractional cubic-quartic nonlinear Schrodinger equation with dierent laws of nonlinearity, Computational Methods for Dierential Equations, 10(3) (2022), 701-715. [21] T. Mathanaranjan, Dipankar Kumar, Hadi Rezazadeh, and Lanre Akinyemi, Optical solitons in metamaterials with third and fourth order dispersions, Optical and Quantum Electronics, 54(5) (2022), 271. [22] T. Mathanaranjan and Dayalini Vijayakumar, New soliton solutions in nano-bers with space-time fractional derivatives, Fractals, 30(7) (2022), 2250141. [23] T. Mathanaranjan, Optical solitons and stability analysis for the new (3+ 1)-dimensional nonlinear Schordinger equation, Journal of Nonlinear Optical Physics & Materials, 32(2) (2023), 2350016. [24] T. Mathanaranjan, New Jacobi elliptic solutions and other solutions in optical metamaterials having higher-order dispersion and its stability analysis, International Journal of Applied and Computational Mathematics,9(5) (2023), 66. [25] T. Mathanaranjan, M. S. Hashemi, H. Rezazadeh, L. Akinyemi, and A. Bekir, Chirped optical solitons and stability analysis of the nonlinear Schordinger equation with nonlinear chromatic dispersion, Communications in Theoretical Physics, 75(8) (2023), 085005. [26] T. Mathanaranjan, Optical soliton, linear stability analysis and conservation laws via multipliers to the integrable Kuralay equation, Optik, 290 (2023), 171266. [27] S. C. Mohapatra and C. Guedes Soares, Comparing solutions of the coupled Boussinesq equations in shallow water, In Maritime Technology and Engineering; Guedes Soares, C., Santos, T.A., Eds.; Taylor & Francis Group: London, UK, (2015), 947-954, [28] S. C. Mohapatra, R. B. Fonseca, and C. Guedes Soares, A comparison between analytical and numerical simulations of solutions of the coupled Boussinesq equations, In Maritime Technology and Engineering; Guedes Soares, C., Santos, T.A., Eds.; Taylor & Francis Group: London, UK, (2016), 1175-1180. [29] S. C. Mohapatra, R. B. Fonseca, and C. Guedes Soares, Comparison of analytical and numerical simulations of long nonlinear internal waves in shallow water, J. Coast. Res., 34 (2018), 928-938. [30] M. Toda, Studies of a non-linear lattice, Phys. Rep, 18(C) (1975), 1-123. [31] J. Vega-Guzman, M. F. Mahmood, Qin Zhou, Houria Triki, Ahmed H. Arnous, Anjan Biswas, Seithuti P. Moshokoa, and Milivoj Belic. Solitons in Nonlinear Directional Couplers with Optical Metamaterials, Nonlinear Dynamics, 87(1) (2016), 427-458. [32] N. M. Ygamurlu and A. S. Karakas, A novel perspective for simulations of the MEW equation by trigonometric cubic B-spline collocation method based on Rubin-Graves type linearization, Computational Methods for Dierential E quations, 10(4) (2022), 1046-1058. [33] Yun-Hui Zhao, T. Mathanaranjan, Hadi Rezazadeh, Lanre Akinyemi, and Mustafa Inc, New solitary wave solutions and stability analysis for the generalized (3+ 1)-dimensional nonlinear wave equation in liquid with gas bubbles, Results in Physics, 43 (2022), 106083.
آمار تعداد مشاهده مقاله: 287 تعداد دریافت فایل اصل مقاله: 497

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

آمار

Solitary waves with two new nonlocal boussinesq types equations using a couple of integration schemes