10.1007/s40096-020-00373-2

New strategic method for fractional mitigating internet bottleneck with quadratic–cubic nonlinearity

  • Jalil Manafian*1,
  • Onur Alp Ilhan2,
  • Sherin Youns Mohyaldeen3,
  • Subhiya M. Zeynalli4,
  • Gurpreet Singh5,
  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, IR
  2. Department of Mathematics, Faculty of Education, Erciyes University, Melikgazi-Kayseri, 38039, TR
  3. Business Administration Department, Zakho Technical Institute, Duhok Polytechnic University, Duhok, Kurdistan Region, IQ
  4. Ganja State University, Ganja, AZ
  5. Department of Mathematics, Sant Baba Bhag Singh University, Jalandhar, 144030, IN

Published in Issue 2021-01-16

How to Cite

Manafian, J., Ilhan, O. A., Mohyaldeen, S. Y., Zeynalli, S. M., & Singh, G. (2021). New strategic method for fractional mitigating internet bottleneck with quadratic–cubic nonlinearity. Mathematical Sciences, 15(4 (December 2021). https://doi.org/10.1007/s40096-020-00373-2
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Abstract

Abstract In this article, the mitigating Internet bottleneck including quadratic–cubic nonlinearity containing the ρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho$$\end{document} -derivative has been considered that describes the control of Internet traffic. This equation is analyzed utilizing two integration schemes, videlicet, the extended sinh-Gordon equation expansion technique and improved tan(Ξ/2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tan (\Xi /2)$$\end{document} -expansion technique. Various kinds of traveling wave solutions by employing these schemes are presented: solitary, topological, periodic, kink-periodic, and soliton wave solutions. Moreover, the plenty of available solutions with guaranteed conditions are also presented. The restriction conditions for the existence of valid solutions are as well as listed. In order to shed more light on these novel solutions, graphical features 3D, 2D, and density with some suitable choice of parameter values have been depicted. The outcome indicates that the mitigating Internet bottleneck is used as an amplifying model in the applied sciences.

Keywords

  • Mitigating Internet bottleneck,
  • Quadratic–cubic nonlinearity,
  • Control Internet traffic,
  • The extended sinh-Gordon equation expansion technique

References

  1. Manafian and Lakestani (2015) Optical solitons with Biswas–Milovic equation for Kerr law nonlinearity (pp. 1-12) https://doi.org/10.1140/epjp/i2015-15061-1
  2. Tahir and Awan (2020) Optical dark and singular solitons to the Biswas–Arshed equation in birefringent fibers without four-wave mixing https://doi.org/10.1016/j.ijleo.2020.164421
  3. Korpinar et al. (2019) New solutions of the fractional Boussinesq-like equations by means of conformable derivatives https://doi.org/10.1016/j.rinp.2019.102339
  4. Manafian and Heidari (2019) Periodic and singular kink solutions of the Hamiltonian amplitude equation 4(2) (pp. 134-149)
  5. Manafian (2016) Optical soliton solutions for Schrödinger type nonlinear evolution equations by the tan(ϕ/2)documentclass[12pt]{minimal}
  6. usepackage{amsmath}
  7. usepackage{wasysym}
  8. usepackage{amsfonts}
  9. usepackage{amssymb}
  10. usepackage{amsbsy}
  11. usepackage{mathrsfs}
  12. usepackage{upgreek}
  13. setlength{oddsidemargin}{-69pt}
  14. begin{document}$$tan(phi /2)$$end{document}-expansion method (pp. 4222-4245) https://doi.org/10.1016/j.ijleo.2016.01.078
  15. Kirane and Ragoub (2015) Nonexistence results for a pseudo-hyperbolic equation in the Heisenberg group (pp. 1-9)
  16. Al-Qurashia and Ragoub (2016) Nonexistence of solutions to a fractional differential boundary value problem (pp. 2233-2243) https://doi.org/10.22436/jnsa.009.05.27
  17. Baskonus and Bulut (2016) Exponential prototype structures for (2+1)-dimensional Boiti–Leon–Pempinelli systems in mathematical physics (pp. 201-208) https://doi.org/10.1080/17455030.2015.1132860
  18. Baskonus et al. (2016) New travelling wave prototypes to the nonlinear Zakharov–Kuznetsov equation with power law nonlinearity (pp. 67-76)
  19. Dehghan et al. (2010) Solving nonlinear fractional partial differential equations using the homotopy analysis method (pp. 448-479) https://doi.org/10.1002/num.20460
  20. Dehghan et al. (2011) Analytical treatment of some partial differential equations arising in mathematical physics by using the Exp-function method (pp. 2965-2981) https://doi.org/10.1142/S021797921110148X
  21. Manafian (2018) Novel solitary wave solutions for the (3+1)-dimensional extended Jimbo–Miwa equations 76(5) (pp. 1246-1260) https://doi.org/10.1016/j.camwa.2018.06.018
  22. Kudryashov (2020) Highly dispersive optical solitons of the generalized nonlinear eighth-order Schrödinger equation https://doi.org/10.1016/j.ijleo.2020.164335
  23. Aslan and Inc (2019) Optical soliton solutions of the NLSE with quadratic-cubic-Hamiltonian perturbations and modulation instability analysis https://doi.org/10.1016/j.ijleo.2019.04.008
  24. Seadawy and Manafian (2018) New soliton solution to the longitudinal wave equation in a magneto–electro–elastic circular rod (pp. 1158-1167)
  25. Zhou (2016) Optical solitons in medium with parabolic law nonlinearity and higher order dispersion (pp. 52-59) https://doi.org/10.1080/17455030.2014.956847
  26. Manafian et al. (2020) Investigating lump and its interaction for the third-order evolution equation arising propagation of long waves over shallow water (pp. 289-301) https://doi.org/10.1016/j.euromechflu.2020.04.013
  27. Yildirim (2019) Optical solitons to Sasa–Satsuma model in birefringent fibers with modified simple equation approach (pp. 197-204) https://doi.org/10.1016/j.ijleo.2019.03.022
  28. El-Sheikh et al. (2019) Optical solitons and other solutions in birefringent fibers with Biswas–Arshed equation by Jacobi’s elliptic function approach https://doi.org/10.1016/j.ijleo.2019.163546
  29. Bhrawy et al. (2014) Optical soliton perturbation with spatio-temporal dispersion in parabolic and dual-power law media by semi-inverse variational principle (pp. 4945-4950) https://doi.org/10.1016/j.ijleo.2014.04.024
  30. Rezazadeh (2018) Mitigating Internet bottleneck with fractional temporal evolution of optical solitons having quadratic-cubic nonlinearity (pp. 84-92) https://doi.org/10.1016/j.ijleo.2018.03.006
  31. Ghanbari et al. (2019) Oblique optical solutions of mitigating internet bottleneck with quadratic-cubic nonlinearity 33(1950224) (pp. 1-18)
  32. Islam et al. (2017) Optical solitons with time fractional nonlinear Schrödinger equation and competing weakly nonlocal nonlinearity (pp. 562-567) https://doi.org/10.1016/j.ijleo.2016.10.090
  33. Gao et al. (2020) Complex solitons in the conformable (2+1)-dimensional Ablowitz–Kaup–Newell–Segur equation 5(1) (pp. 507-521) https://doi.org/10.3934/math.2020034
  34. Gao et al. (2020) New complex wave patterns to the electrical transmission line model arising in network system 5(3) (pp. 1881-1892) https://doi.org/10.3934/math.2020125
  35. Guirao et al. (2020) Regarding new wave patterns of the newly extended nonlinear (2+1)-dimensional Boussinesq equation with fourth order 8(3) https://doi.org/10.3390/math8030341
  36. Yel et al. (2020) New dark-bright soliton in the shallow water wave model 5(4) (pp. 4027-4044) https://doi.org/10.3934/math.2020259
  37. Gómez et al. (2021) Closed form solutions of the perturbed Gerdjikov–Ivanov equation with variable coefficients 11(1) (pp. 207-218) https://doi.org/10.4208/eajam.230620.070920
  38. Osman et al. (2018) Analytical study of solitons to Benjamin–Bona–Mahony–Peregrine equation with power law nonlinearity by using three methods 80(4) (pp. 267-278)
  39. Inc et al. (2020) New solitary wave solutions for the conformable Klein–Gordon equation with quantic nonlinearity 5(6) (pp. 6972-6984) https://doi.org/10.3934/math.2020447
  40. Jena et al. (2020) On the solution of time-fractional dynamical model of Brusselator reaction-diffusion system arising in chemical reactions 43(7) (pp. 3903-3913)
  41. Eslami and Rezazadeh (2016) The first integral method for Wu–Zhang system with conformable time-fractional derivative (pp. 475-485) https://doi.org/10.1007/s10092-015-0158-8
  42. Atangana and Baleanu (2016) New fractional derivatives with nonlocal and non-singular kernel. Theory and application to heat transfer model (pp. 763-769) https://doi.org/10.2298/TSCI160111018A
  43. Biswas et al. (2014) Bright and dark solitons in optical metamaterials (pp. 3299-3302) https://doi.org/10.1016/j.ijleo.2013.12.061
  44. Biswas et al. (2014) Singular solitons in optical metamaterials by Ansatz method and simplest equation approach (pp. 1550-1555) https://doi.org/10.1080/09500340.2014.944357
  45. Kumar et al. (2018) New closed form soliton and other solutions of the Kundu–Eckhaus equation via the extended sinh-Gordon equation expansion method (pp. 159-167) https://doi.org/10.1016/j.ijleo.2018.01.137