New Soliton and Periodic Wave Solutions to the Fractional DGH Equation Describing Water Waves in a Shallow Regime

• S. Saha Ray ^[1]
  1. [1] National Institute Of Technology

     National Institute Of Technology

     Japón

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 4, 2022
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • In this paper, the auxiliary equation method is proposed to find the explicit solutions of the space-time fractional Dullin-Gottwald-Holm equation. Many new soliton and periodic wave solutions to this equation have been determined using the proposed auxiliary equation method. The obtained solutions might play a significant role in shallow water wave propagation. The results manifest that the proposed method is more useful and efficacious than other direct analytical methods. The results also demonstrate that the present technique is a simple and convenient tool for exploring new travelling wave solutions to the currently studied equation.

• Referencias bibliográficas
  • 1. Debnath, L.: Nonlinear Partial Differential Equations for Scientists and Engineers. Birkhäuser, Boston (2005)
  • 2. Wazwaz, A.M.: Partial Differential Equations and Solitary Waves Theory. Springer, Berlin (2009)
  • 3. Saha Ray, S.: Fractional Calculus with Applications for Nuclear Reactor Dynamics. CRC Press, New York (2015)
  • 4. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)
  • 5. Herrmann, R.: Fractional calculus: an introduction for physicists. World Scientific, Singapore (2011)
  • 6. Atangana, A.: Fractional Operators with Constant and Variable Order with Application to Geohydrology. Elsevier, London (2017)
  • 7. Saha Ray, S., Gupta, A.K.: Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations. Chapman and...
  • 8. Saha Ray, S., Sahoo, S.: Generalized Fractional Order Differential Equations Arising in Physical Models. CRC Press, Boca Raton (2018)
  • 9. Saha Ray, S.: Nonlinear Differential Equations in Physics. Springer, Singapore (2020)
  • 10. Saha Ray, S.: Exact solutions for time-fractional diffusion-wave equations by decomposition method. Phys. Scr. 75, 53–61 (2007)
  • 11. Khan, Y., Faraz, N., Yildirim, A., Wu, Q.: Fractional variational iteration method for fractional initialboundary value problems arising...
  • 12. Saha Ray, S.: Soliton solutions of nonlinear and nonlocal sine-gordon equation involving riesz space fractional derivative. Z. Naturforsch....
  • 13. Bekir, A., Güner, Ö., Ünsal, Ö.: The first integral method for exact solutions of nonlinear fractional differential equations. J. Comput....
  • 14. Saha Ray, S.: New exact solutions of nonlinear fractional acoustic wave equations in ultrasound. Comput. Math. Appl. 71, 859–868 (2016)
  • 15. Bekir, A., Aksoy, E., Cevikel, A.C.: Exact solutions of nonlinear time fractional partial differential equations by sub-equation method....
  • 16. Saha Ray, S., Sahoo, S.: Improved fractional sub-equation method for (3+1)-dimensional generalized fractional KdV-Zakharov-Kuznetsov...
  • 17. Bekir, A., Guner, O., Cevikel, A.C.: The fractional complex transforms and exp-function methods for fractional differential equations....
  • 18. Bekir, A., Guner, O., Bhrawy, A.H., Biswas, A.: Solving nonlinear fractional differential equations using exp-function and -expansion...
  • 19. Saha Ray, S.: New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods. Chin. Phys. B. 25, 040204 (2016)
  • 20. Zheng, B., Feng, Q.: (2014): The Jacobi elliptic equation method for solving fractional partial differential equations. Adv. Differ. Equ....
  • 21. Khan, Y., Taghipour, R., Falahian, M., Nikkar, A.: A new approach to modified regularized long wave equation. Neural. Comput. Appl. 23,...
  • 22. Khan, Y., Faraz, N.: Simple use of the Maclaurin series method for linear and non-linear differential equations arising in circuit analysis....
  • 23. Sayevand, K., Khan, Y., Moradi, E., Fardi, M.: Finding the generalized solitary wave solutions within the -expansion method. CMES - Comput....
  • 24. Khan, Y.: Fractal modification of complex Ginzburg-Landau model arising in the oscillating phenomena. Res. Phys. 18, 103324 (2020)
  • 25. Khan, Y.: A novel soliton solutions for the fractal Radhakrishnan–Kundu–Lakshmanan model arising in birefringent fibers. Opt. Quantum...
  • 26. Khan, Y.: A novel type of soliton solutions for the Fokas-Lenells equation arising in the application of optical fibers. Mod. Phys. Lett....
  • 27. Khan, Y.: Novel soliton solutions of the fractal Biswas-Milovic model arising in Photonics. Int. J. Mod. Phys. B. 35, 2150001 (2021)
  • 28. Khan, Y.: A variational approach for novel solitary solutions of FitzHugh–Nagumo equation arising in the nonlinear reaction–diffusion...
  • 29. Khan, Y.: A new necessary condition of soliton solutions for Kawahara equation arising in physics. Optik 155, 273–275 (2018)
  • 30. Kaabar, M.K.A., Kaplan, M., Siri, Z.: New exact soliton solutions of the (3+1)-dimensional conformable Wazwaz-Benjamin-Bona-Mahony...
  • 31. Kumar, D., Hosseini, K., Kaabar, M.K.A., Kaplan, M., Salahshour, S.: On some novel solution solutions to the generalized Schrödinger-Boussinesq...
  • 32. Akbulut, A., Kaplan, M., Kaabar, M.K.A.: New conservation laws and exact solutions of the special case of the fifth-order KdV equation....
  • 33. Dullin, H.R., Gottwald, G.A., Holm, D.D.: An integrable shallow water equation with linear and nonlinear dispersion. Phys. Rev. Lett....
  • 34. Xiao, G.C., Xian, D.Q., Liu, X.Q.: Application of Exp-function method to Dullin–Gottwald–Holm equation. Appl. Math. Comput. 210, 536–541...
  • 35. Meng, Q., He, B., Long, Y., Li, Z.: New exact periodic wave solutions for the Dullin–Gottwald–Holm equation. Appl. Math. Comput. 218,...
  • 36. Bilal, M., Seadawy, A.R., Younis, M., Rizvi, S.T.R., Zahed, H.: Dispersive of propagation wave solutions to unidirectional shallow water...
  • 37. Younis, M., Seadawy, A.R., Sikandar, I., Baber, M.Z., Ahmed, N., Rizvi, S.T.R., Althobaiti, S.: Nonlinear dynamical study to time fractional...
  • 38. Saha Ray, S., Sagar, B.: Numerical solution of fractional Dullin–Gottwald–Holm equation for solitary shallow water waves. Numer. Methods...
  • 39. Ma, H.C., Yu, Y.D., Ge, D.J.: The auxiliary equation method for solving the Zakharov-Kuznetsov (ZK) equation. Comput. Math. with Appl....
  • 40. Akbulut, A., Kaplan, M.: Auxiliary equation method for time-fractional differential equations with conformable derivative. Comput. Math....
  • 41. Rezazadeh, H., Korkmaz, A., Eslami, M., Mirhosseini-Alizamini, S.M.: A large family of optical solutions to Kundu-Eckhaus model by a new...
  • 42. Saha Ray, S.: Dispersive optical solitons of time-fractional Schrödinger-Hirota equation in nonlinear optical fibers. Physica A. 537,...
  • 43. Guner, O.: New exact solutions to the space–time fractional nonlinear wave equation obtained by the ansatz and functional variable methods....