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

 آمار

تعداد نشریات45
تعداد شماره‌ها1,456
تعداد مقالات17,804
تعداد مشاهده مقاله58,081,784
تعداد دریافت فایل اصل مقاله19,606,466
Ur Rehman, Hamood, Iqbal, Ifrah, Eslami, Mostafa, Mirzazadeh, Mohammad, Jedi Abduridha, Sajjad A., Hashemi, Mir Sajjad. (1403). Extended hyperbolic function method for the model having cubic-quintic-septimal nonlinearity in weak nonlocal media. سامانه مدیریت نشریات علمی, 13(1), 271-281. doi: 10.22034/cmde.2024.57337.2396
Hamood Ur Rehman; Ifrah Iqbal; Mostafa Eslami; Mohammad Mirzazadeh; Sajjad A. Jedi Abduridha; Mir Sajjad Hashemi. "Extended hyperbolic function method for the model having cubic-quintic-septimal nonlinearity in weak nonlocal media". سامانه مدیریت نشریات علمی, 13, 1, 1403, 271-281. doi: 10.22034/cmde.2024.57337.2396
Ur Rehman, Hamood, Iqbal, Ifrah, Eslami, Mostafa, Mirzazadeh, Mohammad, Jedi Abduridha, Sajjad A., Hashemi, Mir Sajjad. (1403). 'Extended hyperbolic function method for the model having cubic-quintic-septimal nonlinearity in weak nonlocal media', سامانه مدیریت نشریات علمی, 13(1), pp. 271-281. doi: 10.22034/cmde.2024.57337.2396
Ur Rehman, Hamood, Iqbal, Ifrah, Eslami, Mostafa, Mirzazadeh, Mohammad, Jedi Abduridha, Sajjad A., Hashemi, Mir Sajjad. Extended hyperbolic function method for the model having cubic-quintic-septimal nonlinearity in weak nonlocal media. سامانه مدیریت نشریات علمی, 1403; 13(1): 271-281. doi: 10.22034/cmde.2024.57337.2396

Extended hyperbolic function method for the model having cubic-quintic-septimal nonlinearity in weak nonlocal media

Computational Methods for Differential Equations
مقاله 20، دوره 13، شماره 1، فروردین 2025، صفحه 271-281    اصل مقاله (2.09 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.57337.2396
نویسندگان
Hamood Ur Rehman1؛ Ifrah Iqbal1؛ Mostafa Eslami* 2؛ Mohammad Mirzazadeh3؛ Sajjad A. Jedi Abduridha4؛ Mir Sajjad Hashemi5
1Department of Mathematics, University of Okara, Okara, Pakistan.
2Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
3Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran.
4Department of Mathematics, Faculty of Basic Education, University of Kufa, Najaf, Iraq.
5Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, Iran.
چکیده
Optical solitons are self-trapped light beams that maintain their shape and transverse dimension during propagation. This paper investigates the propagation of solitons in an optical material with a weak nonlocal media, modeled by a cubic-quintic-septimal nonlinearity. The dynamics of solitons in optical waveguides are described by the cubic nonlinear Schrödinger equation and its extensions. This equation model applies to both the spatial propagation of beams and the temporal propagation of pulses in a medium exhibiting cubic nonlinearity. The novelty of the paper lies in the application of the extended hyperbolic function method to derive soliton solutions in optical materials with weak nonlocal media in the form of the periodic, bright, kink, and singular type solitons. The obtained solutions provide explicit expressions for the behavior of optical waves in media. These results shed light on the dynamics of nonlinear waves in optical materials and contribute to a better understanding of soliton propagation. The findings contribute to a more comprehensive understanding of the role of nonlocal nonlinearity and time constants in soliton solutions. Our findings provide a better understanding of the dynamics of the nonlinear waves in optical media and have many application for the field of optical communication and signal processing. The role of nonlocal nonlinearity and time constant on soliton solutions is also discussed with the help of graphs.
کلیدواژه‌ها
Optical solitons؛ Nonlinear Schrödinger equation (NLSE)؛ Solitons؛ Nonlocal nonlinearity
مراجع
  • [1] J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, and P. Smith, Experimental observation of spatial soliton interactions, Optics letters, 16(1) (1991), 15–17.
  • [2] L. Akinyemi, A. Houwe, S. Abbagari, A. M. Wazwaz, H. M. Alshehri, and M. Osman, Effects of the higher order dispersion on solitary waves and modulation instability in a monomode fiber, Optik, 288 (2023), 171202.
  • [3] K. K. Ali, M. A. Abd El Salam, E. M. Mohamed, B. Samet, S. Kumar, and M. Osman, Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using chebyshev series, Advances in Difference Equations, 2020(1) (2020), 1–23.
  • [4] A. U. Awan, M. Tahir, and H. U. Rehman, Singular and bright-singular combo optical solitons in birefringent fibers to the biswas-arshed equation, Optik, 210 (2020), 164489.
  • [5] Z. Chen, M. Segev, and D. N. Christodoulides, Optical spatial solitons: historical overview and recent advances, Reports on Progress in Physics, 75(8) (2012), 086401.
  • [6] Y. Chu, M. M. Khater, and Y. Hamed, Diverse novel analytical and semi-analytical wave solutions of the generalized (2 + 1)-dimensional shallow water waves model, AIP Advances, 11(1) (2021), 015223.
  • [7] Y. Chu, M. A. Shallal, S. M. Mirhosseini-Alizamini, H. Rezazadeh, S. Javeed, and D. Baleanu, Application of modified extended tanh technique for solving complex ginzburg-landau equation considering kerr law nonlinearity, Computers, Materials & Continua, 66(2) (2021), 1369–1377.
  • [8] C. B. Clausen, O. Bang, and Y. S. Kivshar, Spatial solitons and induced kerr effects in quasi-phase-matched quadratic media, Physical review letters, 78(25) (1997), 4749.
  • [9] C. Conti, M. Peccianti, and G. Assanto, Observation of optical spatial solitons in a highly nonlocal medium, Physical review letters, 92(11) (2004), 113902.
  • [10] H. Ding-Jiang and Z. Hong-Qing, Extended hyperbola function method and its application to nonlinear equations, Communications in Theoretical Physics, 41(6) (2004), 801.
  • [11] G. C. Duree Jr, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Observation of self-trapping of an optical beam due to the photo refractive effect, Physical review letters, 71(4) (1993), 533.
  • [12] G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, andA. Yariv, Dark photo refractive spatial solitons and photo refractive vortex solitons, Physical review letters, 74 (11) (1995), 1978.
  • [13] M. R. A. Fahim, P. R. Kundu, M. E. Islam, M. A. Akbar, and M. Osman,Wave profile analysis of a couple of (3+1)dimensional nonlinear evolution equations by sine-gordon expansion approach, Journal of Ocean Engineering and Science, 7(3) (2022), 272–279.
  • [14] X. Gao and J. Zeng, Two-dimensional matter-wave solitons and vortices in competing cubic-quintic nonlinear lattices, Frontiers of Physics, 13(1) (2018), 130501.
  • [15] M. S. Hashemi and M. Mirzazadeh, Optical solitons of the perturbed nonlinear schr¨o dinger equation usinglie symmetry method, Optik, 281 (2023), 170816.
  • [16] Z. Hong, H. Ji-Guang, W. Wei-Tao, and A. Hong-Yong, Applications of extended hyperbolic function method for quintic discrete nonlinear schrödinger equation, Communications in Theoretical Physics, 47(3) (2007), 474.
  • [17] Y. Huang and Y. Shang, The extended hyperbolic function method for generalized forms of nonlinear heat conduction and huxley equations, Journal of Applied Mathematics, 2012 (2012).
  • [18] M. S. Iqbal, M. S. Hashemi, R. Naeem, M. A. Tarar, M. Farheen, and M. Inc, Construction of solitary wave solutions of bi-harmonic coupled schr¨odinger system through φ6-methodology, Optical and Quantum Electronics, 55(5) (2023), 404.
  • [19] M. A. Iqbal, M. M. Miah, M. M. Rasid, H. M. Alshehri, and M. Osman, An investigation of two integro-differential kp hierarchy equations to find out closed form solitons in mathematical physics, Arab Journal of Basic and Applied Sciences, 30(1) (2023), 535–545.
  • [20] H. F. Ismael, H. Bulut, C. Park, and M. Osman, M-lump, n-soliton solutions, and the collision phenomena for the (2 + 1)-dimensional date-jimbo-kashiwara-miwa equation, Results in Physics, 19 (2020), 103329.
  • [21] 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(07) (2022), 2250098.
  • [22] M. Jafari, S. Mahdion, A. Akgu¨l, and S. M. Eldin, New conservation laws of the boussinesq and generalized kadomtsev–petviashvili equations via homotopy operator, Results in Physics, 47 (2023), 106369.
  • [23] 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.
  • [24] Y. S. Kivshar and G. P. Agrawal, Optical solitons: from fibers to photonic crystals, Academic press, 2003.
  • [25] D. Kumar, C. Park, N. Tamanna, G. C. Paul, and M. Osman, Dynamics of two-mode sawada-kotera equation: Mathematical and graphical analysis of its dual-wave solutions, Results in Physics, 19 (2020), 103581.
  • [26] S. Kumar, M. Niwas, M. Osman, and M. Abdou, Abundant different types of exact soliton solution to the (4+ 1)-dimensional fokas and (2+ 1)-dimensional breaking soliton equations, Communications in Theoretical Physics, 73(10) (2021), 105007.
  • [27] S. Malik, M. S. Hashemi, S. Kumar, H. Rezazadeh, W. Mahmoud, and M. Osman, Application of new kudryashov method to various nonlinear partial differential equations, Optical and Quantum Electronics, 55(1) (2023), 8.
  • [28] A. Messouber, H. Triki, Y. Liu, A. Biswas, Y. Yıldırım, A. A. Alghamdi, and Q. Zhou, Chirped spatial solitons on a continuous-wave background in weak nonlocal media with polynomial law of nonlinearity, Physics Letters A, 467 (2023), 128731.
  • [29] G. D. McDonald, C. C. Kuhn, K. S. Hardman, S. Bennetts, P. J. Everitt, P. A. Altin, J. E. Debs, J. D. Close, and N. P. Robins, Bright solitonic matter-wave interferometer, Physical review letters, 113(1) (2014), 013002.
  • [30] M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, All-optical switching and logic gating with spatial solitons in liquid crystals, Applied Physics Letters, 81(18) (2002), 3335–3337.
  • [31] R. U. Rahman, M. M. M. Qousini, A. Alshehri, S. M. Eldin, K. El-Rashidy, and M. Osman, Evaluation of the performance of fractional evolution equations based on fractional operators and sensitivity assessment, Results in Physics, 49 (2023), 106537.
  • [32] H. U. Rehman, M. Tahir, M. Bibi, and Z. Ishfaq, Optical solitons to the biswas–arshed model in birefringent fibers using couple of integration techniques, Optik, 218 (2020), 164894.
  • [33] H. U. Rehman, M. A. Imran, N. Ullah, and A. Akgu¨l, Exact solutions of (2 + 1)-dimensional schrödinger’s hyperbolic equation using different techniques, Numerical Methods for Partial Differential Equations, (2020).
  • [34] H. U. Rehman, A. R. Seadawy, M. Younis, S. Yasin, S. T. Raza, and S. Althobaiti, Monochromatic optical beam propagation of paraxial dynamical model in kerr media, Results in Physics, 31 (2021), 105015.
  • [35] H. U. Rehman, N. Ullah, and M. A. Imran, Optical solitons of biswas-arshed equation in birefringent fibers using extended direct algebraic method, Optik, 226 (2021), 165378.
  • [36] H. U. Rehman, A. U. Awan, E. M. Tag-ElDin, S. E. Alhazmi, M. F. Yassen, and R. Haider, Extended hyperbolic function method for the (2 + 1)-dimensional nonlinear soliton equation, Results in Physics, 40 (2022), 105802.
  • [37] H. U. Rehman, R. Akber, A. M. Wazwaz, H. M. Alshehri, and M. Osman, Analysis of brownian motion instochastic schr¨odinger wave equation using sardar sub-equation method, Optik, 289 (2023), 171305.
  • [38] A. S. Reyna, K. C. Jorge, and C. B. de Arau´jo, Two-dimensional solitons in a quintic-septimal medium, Physical Review A, 90(6) (2014), 063835.
  • [39] A. S. Reyna and C. B. de Araujo, Nonlinearity management of photonic composites and observation of spatialmodulation instability due to quintic nonlinearity, Physical Review A, 89 (6) (2014), 063803.
  • [40] A. S. Reyna and C. B. de Araujo, Spatial phase modulation due to quintic and septic nonlinearities inmetal colloids, Optics Express, 22(19) (2014), 22456–22469.
  • [41] A. S. Reyna, B. A. Malomed, and C. B. de Araujo, Stability conditions for one-dimensional optical solitons in cubic-quintic-septimal media, Physical Review A, 92(3) (2015), 033810.
  • [42] A. S. Reyna and C. B. de Araujo, An optimization procedure for the design of all-optical switches basedon metaldielectric nanocomposites, Optics Express, 23(6) (2015), 7659–7666.
  • [43] S. Sahoo, S. Saha Ray, M. A. M. Abdou, M. Inc, and Y. M. Chu, New soliton solutions of fractional jaulent-miodek system with symmetry analysis, Symmetry, 12(6) (2020), 1001.
  • [44] Y. Shang, Y. Huang, and W. Yuan, The extended hyperbolic functions method and new exact solutions to the zakharov equations, Applied Mathematics and Computation, 200(1) (2008), 110–122.
  • [45] M. Soljacic, S. Sears, and M. Segev, Self-trapping of “necklace” beams in self-focusing kerr media, Physical review letters, 81(22) (1998), 4851.
  • [46] A. M. Sultan, D. Lu, M. Arshad, H. U. Rehman, and M. S. Saleem, Soliton solutions of higher order dispersive cubic-quintic nonlinear schr¨odinger equation and its applications, Chinese Journal of Physics, 67 (2020), 405–413.
  • [47] M. Tiemann, T. Halfmann, and T. Tschudi, Photo refractive spatial solitons as wave guiding elements for optical telecommunication, Optics Communications, 282(17) (2009), 3612–3619.
  • [48] H. Triki, K. Porsezian, P. T. Dinda, and P. Grelu, Dark spatial solitary waves in a cubic-quintic-septimal nonlinear medium, Physical Review A, 95 (2) (2017), 023837.
  • [49] A. Tripathy, S. Sahoo, H. Rezazadeh, Z. Izgi, and M. Osman, Dynamics of damped and undamped wave natures in ferromagnetic materials, Optik, 281 (2023), 170817.
  • [50] N. Ullah, H. U. Rehman, M. Imran, and T. Abdeljawad, Highly dispersive optical solitons with cubic lawand cubic-quintic-septic law nonlinearities, Results in Physics, 17 (2020), 103021.
  • [51] N. Ullah, M. I. Asjad, T. Muhammad, and A. Akgül, Analysis of power law non-linearity in solitonic solutions using extended hyperbolic function method, (2022).
  • [52] S. W. Yao, N. Ullah, H. U. Rehman, M. S. Hashemi, M. Mirzazadeh, and M. Inc, Dynamics on novel wave structures of non-linear schro¨dinger equation via extended hyperbolic function method, Results in Physics, 48 (2023), 106448.
  • [53] M. Younis, M. Iftikhar, and H. U. Rehman, Exact solutions to the nonlinear schrödinger and eckhaus equations by modified simple equation method, Journal of Advanced Physics, 3(1) (2014), 77–79.
  • [54] Q. Zhou, D. Yao, S. Ding, Y. Zhang, F. Chen, F. Chen, and X. Liu, Spatial optical solitons in fifth order and seventh order weakly nonlocal nonlinear media, Optik, 124(22) (2013), 5683–5686.
آمار
تعداد مشاهده مقاله: 613
تعداد دریافت فایل اصل مقاله: 971


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب