Skip to main content
SpringerLink
Log in

Oblique Traveling Wave Closed-Form Solutions to Space-Time Fractional Coupled Dispersive Long Wave Equation Through the Generalized Exponential Expansion Method

  • Original Paper
  • Published:
International Journal of Applied and Computational Mathematics Aims and scope Submit manuscript

Abstract

This work concerned with the oblique traveling wave solutions of coupled space-time fractional (2 + 1)-dimensional dispersive long wave equations (DLWE) for understanding the basic features of resonance wave dynamics in science and engineering, mainly in water wave dynamics. The generalized exp(− \({\Psi }\)(ζ))-expansion scheme mutually by means of conformable derivatives is implemented to seek several types of faithful solutions of coupled DLWE. The oblique traveling wave solutions are displayed in the forms of trigonometric, hyperbolic and rational functions through physical and some supplementary free parameters. It is predicted that the obliqueness is significantly modified the oppositely propagating long waves assuming the suitable values of the parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Data Availability

Enquiries about data availability should be directed to the authors.

References

  1. Sagdeev, R.Z.: Cooperative phenomena and shock waves in collisionless plasmas. Rev. Plasma Phys. 4, 23 (1966)

    Google Scholar 

  2. Hafez, M.G., Talukder, M.R., Ali, M.H.: Two-dimensional nonlinear propagation of ion acoustic waves through KPB and KP equations in weakly relativistic plasmas. Adv. Math. Phys. 2016, 12 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  3. Hafez, M.G., Sakthivel, R., Talukder, M.R.: Some new electrostatic potential functions used to analyze the ion-acoustic waves in a Thomas Fermi plasma with degenerate electrons. Chin. J. Phys. 53, 120901 (2015)

    Google Scholar 

  4. Hafez, M.G., Talukder, M.R., Ali, M.H.: New analytical solutions for propagation of small but finite amplitude ion-acoustic waves in a dense plasma. Wave Random Complex 26, 68 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  5. Maxworthy, T.: On the formation of nonlinear internal waves from the gravitational collapse of mixed regions in two and three dimensions. J. Fluid Mech. 96, 47 (1980)

    Article  Google Scholar 

  6. Tsang, S.C., Chaing, K.S., Chow, K.W.: Soliton interaction in a two-core optical fiber. Opt. Commun. 229, 431 (2004)

    Article  Google Scholar 

  7. Demiray, H.: Head-on collision of solitary waves in fluid-filled elastic tubes. Appl. Math. Lett. 18, 942 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lu, B.: The first integral method for some time fractional differential equations. J. Math. Anal. Appl. 395, 684 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zheng, B.: (G′/G)-expansion method for solving fractional partial differential equations in the theory of mathematical physics. Commun. Theor. Phys. 58, 623 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Liu, W., Chen, K.: The functional variable method for finding exact solutions of some nonlinear time-fractional differential equations. Pramana J. Phys. 81, 3 (2013)

    Article  Google Scholar 

  11. Hafez, M.G.: Exact solutions to the (3 + 1)-dimensional coupled Klein–Gordon–Zakharov equation using exp (− Φ (ξ))-expansion method. Alex. Eng. J. 55, 1635 (2016)

    Article  Google Scholar 

  12. Ferdous, F., Hafez, M.G., Ali, M.Y.: Obliquely propagating wave solutions to conformable time fractional extended Zakharov–Kuzetsov equation via the generalized exp (− Φ (ξ))-expansion method. SeMA 76, 109 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kadkhoda, N., Jafari, H.: Analytical solutions of the Gerdjikov–Ivanov equation by using exp (− φ (ξ))-expansion method. Optik 139, 72 (2017)

    Article  Google Scholar 

  14. Ferdous, F., Hafez, M.G.: Oblique closed form solutions of some important fractional evolution equations via the modified Kudryashov method arising in physical problems. J. Ocean Eng. Sci. 3, 244 (2018)

    Article  Google Scholar 

  15. Hosseini, K., Ansari, R.: New exact solutions of nonlinear conformable time-fractional Boussinesq equations using the modified Kudryashov method. Wave Random Complex 27, 628 (2017)

    Article  MathSciNet  Google Scholar 

  16. Sahoo, S., Ray, S.S.: Improved fractional sub-equation method for (3 + 1)-dimensional generalized fractional KdV–Zakharov–Kuznetsov equations. Comput. Math. Appl. 70, 158 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  17. Abdel-Gawad, H.I., Osman, M.: Exact solutions of the Korteweg–de Vries equation with space and time dependent coefficients by the extended unified method. Indian J. Pure Appl. Math. 45, 1 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  18. Dehghan, M., Manafian, J.: The solution of the variable coefficients fourth-order parabolic partial differential equations by the homotopy perturbation method. Z. Naturforsch 64a, 420 (2009)

    Article  Google Scholar 

  19. Seyedia, S.H., Sarayb, B.N., Nobari, M.R.H.: Multiresolution solution of burgers equation with b-spline wavelet basis. Appl. Math. Comput. 269, 488 (2015)

    MathSciNet  Google Scholar 

  20. Manafian, J.: Novel solitary wave solutions for the -dimensional extended Jimbo-Miwa equations. Comput. Math. Appl. 76, 1246 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  21. Foroutan, M., Manafian, J., Ranjbaran, A.: Lump solution and its interaction to (3 + 1)-D potential-YTSF equation. Nonlinear Dyn. 92, 2077 (2018)

    Article  Google Scholar 

  22. Manafian, J.: Optical solitons with Biswas–Milovic equation for Kerr law nonlinearity. Eur. Phys. J. Plus 130, 1 (2015)

    Article  Google Scholar 

  23. Manafian, J.: Optical soliton solutions for Schrödinger type nonlinear evolution equations by the tan (Φ (ξ)/2)-expansion method. Opt. Int. J. Electr. Opt. 127, 4222 (2016)

    Article  Google Scholar 

  24. Lakestani, M., Manafian, J.: Analytical treatment of nonlinear conformable time-fractional Boussinesq equations by three integration methods. Opt. Quant. Electron 50, 1 (2018)

    Google Scholar 

  25. Marin, M., Öchsner, A.: The effect of a dipolar structure on the Hölder stability in Green–Naghdi thermoelasticity. Contin. Mech. Thermodyn. 29, 1365 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  26. Hassan, M., Marin, M., Alsharif, A., Ellahi, R.: Convective heat transfer flow of nanofluid in a porous medium over wavy surface. Phys. Lett. A 382, 2749 (2018)

    Article  MathSciNet  Google Scholar 

  27. Li, Z.B., He, J.H.: Fractional complex transform for fractional differential equations. Math. Comput. Appl. 15, 970 (2010)

    MathSciNet  MATH  Google Scholar 

  28. Osman, M.S.: Multiwave solutions of time-fractional (2 + 1)-dimensional Nizhnik–Novikov–Veselov equations. Pramana 88, 67 (2017)

    Article  Google Scholar 

  29. Osman, M.S.: Nonlinear interaction of solitary waves described by multi-rational wave solutions of the (2 + 1)-dimensional Kadomtsev–Petviashvili equation with variable coefficients. Nonlinear Dyn. 87, 1209 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  30. Osman, M.S.: On complex wave solutions governed by the 2D Ginzburg–Landau equation with variable coefficients. Optik 156, 169 (2018)

    Article  Google Scholar 

  31. Zheng, B.: Exp-function method for solving fractional partial differential equations. Sci. World J. 2013, 465723 (2013)

    Article  Google Scholar 

  32. Wazwaz, A.M.: Solitary waves solutions for extended forms of quantum Zakharov–Kuznetsov equations. Phys. Scr. 85, 025006 (2012)

    Article  MATH  Google Scholar 

  33. Hafez, M.G., Lu, D.: Traveling wave solutions for space-time fractional nonlinear evolution equations. arXiv:1512.00715 [math.AP] (2015).

  34. Ali, M.N., Osman, M.S., Husnine, S.M.: On the analytical solutions of conformable time-fractional extended Zakharov–Kuznetsov equation through (G′/G2)-expansion method and the modified Kudryashov method. SeMA J. 76, 15 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  35. Ferdous, F., Hafez, M.G.: Nonlinear time fractional Korteweg–de Vries equations for the interaction of wave phenomena in fluid-filled elastic tubes. Eur. Phys. J. Plus 133, 384 (2018)

    Article  Google Scholar 

  36. Khalil, R., Horani, M.A., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  37. Bekir, A., Aksoy, E., Güner, Ö.: A generalized fractional sub-equation method for nonlinear fractional differential equations. AIP Conf. Proc. 1611, 78 (2014)

    Article  Google Scholar 

  38. Yan, Z.Y.: Generalized transformations and abundant new families of exact solutions for (2 + 1)-dimensional dispersive long wave equations. Comput. Math. Appl. 46, 1363 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  39. Yomba, E.: The modified extended Fan’s sub-equation method and its application to (2 + 1)-dimensional dispersive long wave equation. Chaos Soliton Fract. 26, 785 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  40. Chen, Y., Wang, Q.: A series of new soliton-like solutions and double-like periodic solutions of a (2 + 1)-dimensional dispersive long wave equation. Chaos Soliton Fract. 23, 801 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  41. Seyedi, S.H., Saray, B.N., Ramazani, A.: On the multiscale simulation of squeezing nanofluid flow by a highprecision scheme. Powder Technol. 340, 264 (2018)

    Article  Google Scholar 

  42. Ferdous, F., Hafez, M.G., Biswas, A., et al.: Oblique resonant optical solitons with Kerr and parabolic law nonlinearities and fractional temporal evolution by generalized exp (− Φ (ξ))-expansion. Optik 178, 439 (2019)

    Article  Google Scholar 

Download references

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

  1. Department of Mathematics, Chittagong University of Engineering and Technology, Chittagong, 4349, Bangladesh

    F. Ferdous, M. G. Hafez & S. Akther

  2. Port City International University, Chittagong, Bangladesh

    S. Akther

Authors
  1. F. Ferdous
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. G. Hafez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Akther
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. G. Hafez.

Ethics declarations

Conflict of interest

The authors have not disclosed any competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ferdous, F., Hafez, M.G. & Akther, S. Oblique Traveling Wave Closed-Form Solutions to Space-Time Fractional Coupled Dispersive Long Wave Equation Through the Generalized Exponential Expansion Method. Int. J. Appl. Comput. Math 8, 142 (2022). https://doi.org/10.1007/s40819-022-01339-9

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40819-022-01339-9

Keywords

Mathematics Subject Classification

Search

Navigation