Startseite Technik Propagation of dark-bright soliton and kink wave solutions of fluidized granular matter model arising in industrial applications
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Propagation of dark-bright soliton and kink wave solutions of fluidized granular matter model arising in industrial applications

  • Yeşim Sağlam Özkan ORCID logo und Emrullah Yaşar ORCID logo EMAIL logo
Veröffentlicht/Copyright: 24. November 2021
Veröffentlichen auch Sie bei De Gruyter Brill
Informationen für Autor*innen
International Journal of Nonlinear Sciences and Numerical Simulation
Aus der Zeitschrift International Journal of Nonlinear Sciences and Numerical Simulation Band 24 Heft 2

Abstract

The improved tan(φ/2)-expansion, simplest equation, and extended (G′/G)-expansion methods are employed to construct the exact solutions involving parameters of the Van der Waals equation arising in the material industry. This model explains the phase separation phenomenon. Understanding the prominent dynamic and static properties of this model and other models of this type is of great importance for the physical phenomena encountered in many areas of industry. Therefore, for such models, it is also important to obtain guiding solutions in obtaining new information. Many explicit wave solutions consisting of trigonometric, hyperbolic, rational, and exponential functions are found by using analytical techniques. The obtained solutions were verified with Maple by placing them back into the original equations. Moreover, graphical demonstrations for some of the obtained solutions are given.

Keywords: extended (G′/G)-expansion method; ITEM; simplest equation method; van der Waals equation
MSC 2010: 35C07; 35C08
Corresponding author: Emrullah Yaşar, Department of Mathematics, Faculty of Arts and Sciences, Bursa Uludag University, 16059 Bursa, Türkiye, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

[1] P. Agarwal, A. A. Hyder, M. Zakarya, G. AlNemer, C. Cesarano, and D. Assante, “Exact solutions for a class of Wick-type stochastic (3 + 1)-dimensional modified Benjamin–Bona–Mahony equations,” Axioms, vol. 8, no. 4, p. 134, 2019. https://doi.org/10.3390/axioms8040134.Suche in Google Scholar

[2] O. A. Ilhan and J. Manafian, “Analytical treatment in optical metamaterials with anti-cubic law of nonlinearity by improved exp(−ϕ(ξ))-expansion method and extended sinh-Gordon equation expansion method,” Rev. Mexic. Fisica, vol. 65, no. 6, pp. 658–677, 2019. https://doi.org/10.31349/revmexfis.65.658.Suche in Google Scholar

[3] T. A. Sulaiman and H. Bulut, “Boussinesq equations: M-fractional solitary wave solutions and convergence analysis,” J. Ocean Eng. Sci., vol. 4, no. 1, pp. 1–6, 2019. https://doi.org/10.1016/j.joes.2018.12.001.Suche in Google Scholar

[4] U. Younas, A. R. Seadawy, M. Younis, and S. T. R. Rizvi, “Optical solitons and closed form solutions to the (3+ 1)-dimensional resonant Schrödinger dynamical wave equation,” Int. J. Mod. Phys. B, vol. 34, no. 30, p. 2050291, 2020. https://doi.org/10.1142/s0217979220502914.Suche in Google Scholar

[5] H. Bulut, T. A. Sulaiman, H. M. Baskonus, H. Rezazadeh, M. Eslami, and M. Mirzazadeh, “Optical solitons and other solutions to the conformable space–time fractional Fokas–Lenells equation,” Optik, vol. 172, pp. 20–27, 2018. https://doi.org/10.1016/j.ijleo.2018.06.108.Suche in Google Scholar

[6] B. Ayhan and A. Bekir, “The G′G-expansion method for the nonlinear lattice equations,” Commun. Nonlinear Sci. Numer. Simulat., vol. 17, no. 9, pp. 3490–3498, 2012. https://doi.org/10.1016/j.cnsns.2012.01.009.Suche in Google Scholar

[7] A. Ali, A. R. Seadawy, and D. Lu, “New solitary wave solutions of some nonlinear models and their applications,” Adv. Differ. Equ., vol. 2018, no. 1, pp. 1–12, 2018. https://doi.org/10.1186/s13662-018-1687-7.Suche in Google Scholar

[8] A. Kurt, O. Tasbozan, and D. Baleanu, “New solutions for conformable fractional Nizhnik–Novikov–Veselov system via G′/G expansion method and homotopy analysis methods,” Opt. Quant. Electron., vol. 49, no. 10, p. 333, 2017. https://doi.org/10.1007/s11082-017-1163-8.Suche in Google Scholar

[9] X. Wang and J. Zhu, “Broer–Kaup system with corrections via inverse scattering transform,” Adv. Math. Phys., vol. 2020, 2020. https://doi.org/10.1155/2020/7859897.Suche in Google Scholar

[10] R. Hirota, “Exact solution of the Korteweg–de Vries equation for multiple collisions of solitons,” Phys. Rev. Lett., vol. 27, no. 18, p. 1192, 1971. https://doi.org/10.1103/physrevlett.27.1192.Suche in Google Scholar

[11] J. G. Liu, M. Eslami, H. Rezazadeh, and M. Mirzazadeh, “Rational solutions and lump solutions to a non-isospectral and generalized variable-coefficient Kadomtsev–Petviashvili equation,” Nonlinear Dynam., vol. 95, no. 2, pp. 1027–1033, 2019. https://doi.org/10.1007/s11071-018-4612-4.Suche in Google Scholar

[12] J. Manafian and M. Lakestani, “Optical soliton solutions for the Gerdjikov–Ivanov model via tan(ϕ/2)-expansion method,” Optik, vol. 127, no. 20, pp. 9603–9620, 2016. https://doi.org/10.1016/j.ijleo.2016.07.032.Suche in Google Scholar

[13] J. Manafian, M. F. Aghdaei, and M. Zadahmad, “Analytic study of sixth-order thin-film equation by tan(ϕ/2)-expansion method,” Opt. Quant. Electron., vol. 48, no. 8, p. 410, 2016. https://doi.org/10.1007/s11082-016-0683-y.Suche in Google Scholar

[14] N. Raza, J. Afzal, A. Bekir, and H. Rezazadeh, “Improved tan(ϕ/2)-expansion approach for Burgers equation in nonlinear dynamical model of ion acoustic waves,” Braz. J. Phys., vol. 50, no. 3, pp. 254–262, 2020. https://doi.org/10.1007/s13538-020-00743-0.Suche in Google Scholar

[15] Y. S. Özkan and E. Yaşar, “On the exact solutions of nonlinear evolution equations by the improved tan(ϕ/2)-expansion method,” Pramana, vol. 94, no. 1, p. 37, 2020. https://doi.org/10.1007/s12043-019-1883-3.Suche in Google Scholar

[16] C. T. Sendi, J. Manafian, H. Mobasseri, M. Mirzazadeh, Q. Zhou, and A. Bekir, “Application of the ITEM for solving three nonlinear evolution equations arising in fluid mechanics,” Nonlinear Dynam., vol. 95, no. 1, pp. 669–684, 2019. https://doi.org/10.1007/s11071-018-4589-z.Suche in Google Scholar

[17] I. Ali, A. R. Seadawy, S. R. Rizvi, M. Younis, and K. Ali, “Conserved quantities along with painleve analysis and optical solitons for the nonlinear dynamics of Heisenberg ferromagnetic spin chains model,” Int. J. Mod. Phys. B, vol. 34, no. 30, p. 2050283, 2020. https://doi.org/10.1142/s0217979220502835.Suche in Google Scholar

[18] M. Kaplan, A. Bekir, A. Akbulut, and E. Aksoy, “The modified simple equation method for nonlinear fractional differential equations,” Rom. J. Phys., vol. 60, nos 9–10, pp. 1374–1383, 2015.Suche in Google Scholar

[19] E. M. Zayed and M. E. Alngar, “Optical soliton solutions for the generalized Kudryashov equation of propagation pulse in optical fiber with power nonlinearities by three integration algorithms,” Math. Methods Appl. Sci., 2020. https://doi.org/10.1002/mma.6736.Suche in Google Scholar

[20] N. Raza and A. Zubair, “Optical dark and singular solitons of generalized nonlinear Schrödinger’s equation with anti-cubic law of nonlinearity,” Mod. Phys. Lett. B, vol. 33, no. 13, p. 1950158, 2019. https://doi.org/10.1142/s0217984919501586.Suche in Google Scholar

[21] A. R. Seadawy and N. Cheemaa, “Applications of extended modified auxiliary equation mapping method for high-order dispersive extended nonlinear Schrödinger equation in nonlinear optics,” Mod. Phys. Lett. B, vol. 33, no. 18, p. 1950203, 2019. https://doi.org/10.1142/s0217984919502038.Suche in Google Scholar

[22] A. R. Seadawy, A. Ali, and W. A. Albarakati, “Analytical wave solutions of the (2 + 1)-dimensional first integro-differential Kadomtsev–Petviashivili hierarchy equation by using modified mathematical methods,” Results Phys., vol. 15, pp. 102775–102779, 2019. https://doi.org/10.1016/j.rinp.2019.102775.Suche in Google Scholar

[23] M. Mirzazadeh, M. Ekici, A. Sonmezoglu, et al.., “Optical solitons with complex Ginzburg–Landau equation,” Nonlinear Dynam., vol. 85, no. 3, pp. 1979–2016, 2016. https://doi.org/10.1007/s11071-016-2810-5.Suche in Google Scholar

[24] A. Zafar, B. Khalid, A. Fahand, H. Rezazadeh, and A. Bekir, “Analytical behaviour of travelling wave solutions to the van der Waals model,” Int. J. Algorithm. Comput. Math., vol. 6, no. 5, pp. 1–16, 2020. https://doi.org/10.1007/s40819-020-00884-5.Suche in Google Scholar

[25] A. R. Seadawy, D. Kumar, K. Hosseini, and F. Samadani, “The system of equations for the ion sound and Langmuir waves and its new exact solutions,” Results Phys., vol. 9, pp. 1631–1634, 2018. https://doi.org/10.1016/j.rinp.2018.04.064.Suche in Google Scholar

[26] S. T. R. Rizvi, A. R. Seadawy, I. Ali, I. Bibi, and M. Younis, “Chirp-free optical dromions for the presence of higher order spatio-temporal dispersions and absence of self-phase modulation in birefringent fibers,” Mod. Phys. Lett. B, vol. 34, no. 35, p. 2050399, 2020. https://doi.org/10.1142/s0217984920503996.Suche in Google Scholar

[27] A. R. Seadawy, D. Lu, and M. Iqbal, “Application of mathematical methods on the system of dynamical equations for the ion sound and Langmuir waves,” Pramana, vol. 93, no. 1, pp. 1–12, 2019. https://doi.org/10.1007/s12043-019-1771-x.Suche in Google Scholar

[28] N. Zhang, T. C. Xia, and E. G. Fan, “A Riemann–Hilbert approach to the Chen–Lee–Liu equation on the half line,” Acta Math. Appl. Sin. (Engl. Ser.), vol. 34, no. 3, pp. 493–515, 2018. https://doi.org/10.1007/s10255-018-0765-7.Suche in Google Scholar

[29] M. Arshad, A. R. Seadawy, and D. Lu, “Bright–dark solitary wave solutions of generalized higher-order nonlinear Schrödinger equation and its applications in optics,” J. Electromagn. Waves Appl., vol. 31, no. 16, pp. 1711–1721, 2017. https://doi.org/10.1080/09205071.2017.1362361.Suche in Google Scholar

[30] B. B. Hu, T. C. Xia, and W. X. Ma, “Riemann–Hilbert approach for an initial-boundary value problem of the two-component modified Korteweg–de Vries equation on the half-line,” Appl. Math. Comput., vol. 332, pp. 148–159, 2018. https://doi.org/10.1016/j.amc.2018.03.049.Suche in Google Scholar

[31] A. R. Seadawy and N. Cheemaa, “Propagation of nonlinear complex waves for the coupled nonlinear Schrödinger Equations in two core optical fibers,” Phys. Stat. Mech. Appl., vol. 529, p. 121330, 2019. https://doi.org/10.1016/j.physa.2019.121330.Suche in Google Scholar

[32] I. Ahmed, A. R. Seadawy, and D. Lu, “M-shaped rational solitons and their interaction with kink waves in the Fokas–Lenells equation,” Phys. Scripta, vol. 94, no. 5, p. 055205, 2019. https://doi.org/10.1088/1402-4896/ab0455.Suche in Google Scholar

[33] S. T. R. Rizvi, A. R. Seadawy, F. Ashraf, M. Younis, H. Iqbal, and D. Baleanu, “Lump and interaction solutions of a geophysical Korteweg–de Vries equation,” Results Phys., vol. 19, p. 103661, 2020. https://doi.org/10.1016/j.rinp.2020.103661.Suche in Google Scholar

[34] A. R. Seadawy and N. Cheemaa, “Some new families of spiky solitary waves of one-dimensional higher-order K–dV equation with power law nonlinearity in plasma physics,” Indian J. Phys., vol. 94, no. 1, pp. 117–126, 2020. https://doi.org/10.1007/s12648-019-01442-6.Suche in Google Scholar

[35] J. Li and T. Xia, “N-soliton solutions for the nonlocal Fokas–Lenells equation via RHP,” Appl. Math. Lett., vol. 113, p. 106850, 2021. https://doi.org/10.1016/j.aml.2020.106850.Suche in Google Scholar

[36] N. Cheemaa, A. R. Seadawy, and S. Chen, “More general families of exact solitary wave solutions of the nonlinear Schrödinger equation with their applications in nonlinear optics,” Eur. Phys. J. Plus, vol. 133, no. 12, pp. 1–9, 2018. https://doi.org/10.1140/epjp/i2018-12354-9.Suche in Google Scholar

[37] Y. S. Özkan, E. Yaşar, and A. R. Seadawy, “On the multi-waves, interaction and Peregrine-like rational solutions of perturbed Radhakrishnan–Kundu–Lakshmanan equation,” Phys. Scripta, vol. 95, no. 8, p. 085205, 2020. https://doi.org/10.1088/1402-4896/ab9af4.Suche in Google Scholar

[38] S. Bibi, N. Ahmed, U. Khan, and S. T. Mohyud-Din, “Some new exact solitary wave solutions of the Van der Waals model arising in nature,” Results Phys., vol. 9, p. 648, 2018. https://doi.org/10.1016/j.rinp.2018.03.026.Suche in Google Scholar

[39] D. Lu, A. R. Seadawy, and M. A. Khater, “Bifurcations of new multi soliton solutions of the van der Waals normal form for uidized granular matter via six different methods,” Results Phys., vol. 7, p. 2028, 2017. https://doi.org/10.1016/j.rinp.2017.06.014.Suche in Google Scholar

[40] M. Argentina, M. G. Clerc, and R. Soto, “Van der Waals–like transition in fluidized granular matter,” Phys. Rev. Lett., vol. 89, no. 4, p. 044301, 2002. https://doi.org/10.1103/PhysRevLett.89.044301.Suche in Google Scholar PubMed

[41] A. Zafar, B. Khalid, A. Fahand, H. Rezazadeh, and A. Bekir, “Analytical behaviour of travelling wave solutions to the van der Waals model,” Int. J. Algorithm. Comput. Math., vol. 6, no. 5, pp. 1–16, 2020. https://doi.org/10.1007/s40819-020-00884-5.Suche in Google Scholar

[42] A. M. Abourabia and A. M. Morad, “Exact traveling wave solutions of the van der Waals normal form for fluidized granular matter,” Phys. Stat. Mech. Appl., vol. 437, pp. 333–350, 2015. https://doi.org/10.1016/j.physa.2015.06.005.Suche in Google Scholar

[43] N. A. Kudryashov, “Simplest equation method to look for exact solutions of nonlinear differential equations,” Chaos, Solit. Fractals, vol. 24, pp. 1217–1231, 2005. https://doi.org/10.1016/j.chaos.2004.09.109.Suche in Google Scholar

[44] N. A. Kudryashov, “Exact solitary waves of the Fisher equation,” Phys. Lett. A, vol. 342, nos 1–2, pp. 99–106, 2005. https://doi.org/10.1016/j.physleta.2005.05.025.Suche in Google Scholar

[45] S. Guo and Y. Zhou, “The extended G′G-expansion method and its applications to the Whitham–Broer–Kaup–Like equations and coupled Hirota–Satsuma KdV equations,” Appl. Math. Comput., vol. 215, no. 9, pp. 3214–3221, 2010. https://doi.org/10.1016/j.amc.2009.10.008.Suche in Google Scholar

[46] E. M. E. Zayed and M. A. S. El-Malky, “The extended (G′/G)-expansion method and its applications for solving the (3 + 1)-dimensional nonlinear evolution equations in mathematical physics,” Glob. J. Sci. Front. Res. (GJSFR), vol. 11, no. 1, pp. 68–80, 2011.Suche in Google Scholar

[47] A. M. Wazwaz, Partial Differential Equations and Solitary Waves Theory, Berlin, Heidelberg, Springer Science & Business Media, 2010.10.1007/978-3-642-00251-9Suche in Google Scholar
Received: 2021-01-13
Revised: 2021-07-29
Accepted: 2021-11-04
Published Online: 2021-11-24

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Original Research Articles
  3. Numerical solutions for variable-order fractional Gross–Pitaevskii equation with two spectral collocation approaches
  4. Threshold dynamics of an HIV-1 model with both virus-to-cell and cell-to-cell transmissions, immune responses, and three delays
  5. Numerical scheme and analytical solutions to the stochastic nonlinear advection diffusion dynamical model
  6. On modeling column crystallizers and a Hermite predictor–corrector scheme for a system of integro-differential equations
  7. On a discrete fractional stochastic Grönwall inequality and its application in the numerical analysis of stochastic FDEs involving a martingale
  8. A new self adaptive Tseng’s extragradient method with double-projection for solving pseudomonotone variational inequality problems in Hilbert spaces
  9. Solitary waves of the RLW equation via least squares method
  10. Optical solitons and stability regions of the higher order nonlinear Schrödinger’s equation in an inhomogeneous fiber
  11. Weighted pseudo asymptotically Bloch periodic solutions to nonlocal Cauchy problems of integrodifferential equations in Banach spaces
  12. Modified inertial subgradient extragradient method for equilibrium problems
  13. Propagation of dark-bright soliton and kink wave solutions of fluidized granular matter model arising in industrial applications
  14. Existence and uniqueness of positive solutions for fractional relaxation equation in terms of ψ-Caputo fractional derivative
  15. Investigation of nonlinear fractional delay differential equation via singular fractional operator
  16. Travelling peakon and solitary wave solutions of modified Fornberg–Whitham equations with nonhomogeneous boundary conditions
  17. The (3 + 1)-dimensional Wazwaz–KdV equations: the conservation laws and exact solutions
  18. Stability and ψ-algebraic decay of the solution to ψ-fractional differential system
  19. Some new characterizations of a space curve due to a modified frame N ⃗ , C ⃗ , W ⃗ in Euclidean 3-space
  20. Numerical simulation of particulate matter propagation in an indoor environment with various types of heating
  21. Inertial accelerated algorithms for solving split feasibility with multiple output sets in Hilbert spaces
  22. Stability analysis and abundant closed-form wave solutions of the Date–Jimbo–Kashiwara–Miwa and combined sinh–cosh-Gordon equations arising in fluid mechanics
  23. Contrasting effects of prey refuge on biodiversity of species
https://doi.org/10.1515/ijnsns-2021-0016
Schlagwörter für diesen Artikel
extended (G′/G)-expansion method; ITEM; simplest equation method; van der Waals equation

Artikel in diesem Heft

  1. Frontmatter
  2. Original Research Articles
  3. Numerical solutions for variable-order fractional Gross–Pitaevskii equation with two spectral collocation approaches
  4. Threshold dynamics of an HIV-1 model with both virus-to-cell and cell-to-cell transmissions, immune responses, and three delays
  5. Numerical scheme and analytical solutions to the stochastic nonlinear advection diffusion dynamical model
  6. On modeling column crystallizers and a Hermite predictor–corrector scheme for a system of integro-differential equations
  7. On a discrete fractional stochastic Grönwall inequality and its application in the numerical analysis of stochastic FDEs involving a martingale
  8. A new self adaptive Tseng’s extragradient method with double-projection for solving pseudomonotone variational inequality problems in Hilbert spaces
  9. Solitary waves of the RLW equation via least squares method
  10. Optical solitons and stability regions of the higher order nonlinear Schrödinger’s equation in an inhomogeneous fiber
  11. Weighted pseudo asymptotically Bloch periodic solutions to nonlocal Cauchy problems of integrodifferential equations in Banach spaces
  12. Modified inertial subgradient extragradient method for equilibrium problems
  13. Propagation of dark-bright soliton and kink wave solutions of fluidized granular matter model arising in industrial applications
  14. Existence and uniqueness of positive solutions for fractional relaxation equation in terms of ψ-Caputo fractional derivative
  15. Investigation of nonlinear fractional delay differential equation via singular fractional operator
  16. Travelling peakon and solitary wave solutions of modified Fornberg–Whitham equations with nonhomogeneous boundary conditions
  17. The (3 + 1)-dimensional Wazwaz–KdV equations: the conservation laws and exact solutions
  18. Stability and ψ-algebraic decay of the solution to ψ-fractional differential system
  19. Some new characterizations of a space curve due to a modified frame N ⃗ , C ⃗ , W ⃗ in Euclidean 3-space
  20. Numerical simulation of particulate matter propagation in an indoor environment with various types of heating
  21. Inertial accelerated algorithms for solving split feasibility with multiple output sets in Hilbert spaces
  22. Stability analysis and abundant closed-form wave solutions of the Date–Jimbo–Kashiwara–Miwa and combined sinh–cosh-Gordon equations arising in fluid mechanics
  23. Contrasting effects of prey refuge on biodiversity of species
Jetzt anmelden und 20% sparen
Institutioneller Zugang
Wie funktioniert Authentifizierung?
Haben Sie eine Idee, wie wir unsere Website verbessern können?
Bitte schreiben Sie uns.
© 2026 De Gruyter Brill
Heruntergeladen am 5.2.2026 von https://www.degruyterbrill.com/document/doi/10.1515/ijnsns-2021-0016/html
Button zum nach oben scrollen