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Application of mathematical methods for the nonlinear seventh order Sawada-Kotera Ito dynamical wave equation

ABSTRACT
This article deal with finding travelling wave solutions for the seventh order Sawada-Kotera Ito dynamical wave equation which describes the evolution of steeper waves of shorter wavelength than KdV equations using modified extended direct algebraic method. The new solutions derived have various physical structure, we also give graphic representation of the exact and stable solutions.
KEYWORDS
PAPER SUBMITTED: 2019-07-05
PAPER REVISED: 2019-08-10
PAPER ACCEPTED: 2019-08-20
PUBLISHED ONLINE: 2019-10-06
DOI REFERENCE: https://doi.org/10.2298/TSCI190705373A
REFERENCES
  1. Malfliet, W., Hereman, W.,The tanh method: Exact solutions of nonlinear evolution and wave equations, Physica Scripta, 54 (1996),6, pp.563.
  2. Wazwaz, A. M., The tanh-coth and the sech methods for exact solutions of the Jaulent-Miodek equation, Physics Letters A, 366 (2007), 1-2, pp. 85-90.
  3. Wazwaz, A. M., New travelling wave solutions to the Boussinesq and the Klein-Gordon equations, Communications in Nonlinear Science and Numerical Simulation, 13 (2008), 5, pp. 889-901.
  4. Abdou, M., et. al., New application of Exp-function method for improved Boussinesq equation, Physics Letters A, 369 (2007), 5-6, pp. 469-475.
  5. Seadawy, A. R., Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its a solitary wave solutions via mathematical methods , European Physical Journal Plus ,132 (2017) 518.
  6. Tariq K. U. and Seadawy, A. R., Bistable Bright-Dark solitary wave solutions of the (3+1)-Dimensional Breaking Soliton, Boussinesq equation with dual dispersion and modified Korteweg-de Vries-Kadomtsev-Petviashvili equations and their applications, Results in Physics 7 (2017) 1143-1149.
  7. Seadawy, A. R. and K. El-Rashidy, Rayleigh-Taylor instability of the cylindrical flow with mass and heat transfer, The Pramana - Journal of Physics, 87 (2016) 20.
  8. Seadawy, A. R., M. Arshad and D. Lu, Stability analysis of new exact traveling Wave Solutions of new coupled KdV and new coupled Zakharov-Kuznetsov systems, The European Physical Journal Plus, 132 (2017) 162.
  9. Seadawy, A. R., Three-dimensional weakly nonlinear shallow water waves regime and its travelling wave solutions, International Journal of Computational Methods, 15 , 3, (2018) 1850017. .
  10. Khater, A. H., Callebaut D. K and Seadawy, A. R., General Soliton Solutions for Nonlinear Dispersive Waves in Convective Type Instabilities, Physica Scripta, 74 (2006) 384-393.
  11. Helal, M. A. and Seadawy, A. R., Benjamin-Feir-instability in nonlinear dispersive waves, Computers and Mathematics with Applications, 64 (2012) 3557-3568.
  12. Khater, A. H., Callebaut D. K., Helal, M. A. and Seadawy A. R., Variational Method for the Nonlinear Dynamics of an Elliptic Magnetic Stagnation Line, The European Physical Journal D, 39 , (2006) 237-245.
  13. Seadawy A. R., Approximation solutions of derivative nonlinear Schrodinger equation with computational applications by variational method, The European Physical Journal Plus, 130 (2015) 182.
  14. Seadawy A. R., Ion acoustic solitary wave solutions of two-dimensional nonlinear KadomtsevPetviashviliBurgers equation in quantum plasma, Mathematical methods and applied Sciences, 40 , (5), (2017) 1598-1607.
  15. Seadawy, A., New exact solutions for the KdV equation with higher order nonlinearity by using the variational method , Computers and Mathematics with Applications , 62 (2011), 10, pp. 3741-3755.
  16. Kabir, M., Modified Kudryashov method for finding exact solitary wave solutions of higher-order non-linear equations, Mathematical methods in the Applied Sciences, 34 (2011), 2, pp. 213-219.
  17. Seadawy, A., The generalized nonlinear higher order of KdV equations from the higher order nonlinear Schrdinger equation, Optik, 139 (2017), pp. 31-43.
  18. Ganji, D., et. al., New exact solutions for seventh- order SawadaKoteraIto, Lax and KaupKupershmidt equations using exp-function method, Mathematical Methods in the Applied Sciences, 33 (2010), 2, pp.167-176.
  19. Feng, J., New traveling wave solutions to the seventh-order Sawada-Kotera equation, Journal of applied mathematics & informatics, 28 (2010), 5-6, pp.1431-1437.
  20. Shen, Y., et. al., Improved bell-polynomial procedure for the higher-order Korteweg-de Vries equations in fluid dynamics, Applied Mathematics and Computation, 274 (2016), pp. 403-413.
  21. Pomeau, Y., et. al., Structural stability of the Korteweg-de Vries solitons under a singular perturbation, Physica D: Nonlinear Phenomena, 31 (1988), 1, pp. 127-134.
  22. Wazwaz, A. M., The Hirotas bilinear method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera-Kadomtsev-Petviashvili equation, Applied Mathematics and Computation, 200 (2008), 1, pp. 160-166.
  23. Salas, A. H., et. al., Computing exact solutions to a generalized Lax-Sawada-Kotera-Ito seventh-order KdV equation, Mathematical Problems in Engineering, 2010 (2010), pp. 1-7.
  24. Jafari, H., et. al., Application of hes varia-tional iteration method for solving seventh order sawadakotera equations, Applied Mathematical Sciences, 2 (2008), 9-12, pp. 471-477.
  25. El-Sayed, S. M., Kaya, D., An application of the ADM to seven-order SawadaKotara equations, Applied mathematics and computation, 157 (2004), 1, pp. 93-101.
  26. Ganji, D., et. al., HPM and VIM methods for finding the exact solutions of the nonlinear dispersive equations and seventh-order Sawada-Kotera equation, International Journal of Modern Physics B, 23 (2009), 01, pp. 39-52.
  27. Zuhra, S., et. al., Generalized Seventh Order Korteweg-De Vries Equations By Optimal Homotopy Aysmptotic Method, Sci. Int, 27 (2015), 4, pp. 3023-3032.
  28. Kaya, D., Inan, I., On the Sawada-Kotare equation, J. Inst. Math. Comp. Sei, 14 (2001), pp. 117-119.
  29. Hubert, M., et. al., Optical solitons in parabolic law medium with weak non-local nonlinearity using modified extended direct algebraic method, Optik, 161 (2018), pp. 180-186.
  30. Yomba, E., A generalized auxiliary equation method and its application to nonlinear Klein-Gordon and generalized nonlinear Camassa-Holm equations, Physics Letters A, 372 (2008), 7, pp. 1048-1060.
  31. Wang, M., et. al., Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics, Physics Letters A, 216 (1996), 1-5, pp. 67-75.
  32. Wang, M., Exact solutions for a compound KdV-Burgers equation, Physics Letters A, 213 (1996), 5-6, pp. 279-287.
  33. Arora, R., Sharma, H., Application of HAM to seventh order KdV equations, International Journal of System Assurance Engineering and Management, 9 (2018), 1, pp. 131-138.