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Kink wave solutions to KdV-Burgers equation with forcing term

Yusuf Buba Chukkol|Mukhiddin Muminov
대한수학회 (The Korean Mathematical Society)|2020.04|대한수학회논문집 (Communications of the KMS)|제35권 제2호|pp. 685-695|DOI 10.4134/CKMS.c190119

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키워드

KdVB equationRiccati equationsecant hyperbolic ansatzmodified tanh-coth method
주제분류수학

초록

In this paper, we used modified tanh-coth method, combined with Riccati equation and secant hyperbolic ansatz to construct abundantly many real and complex exact travelling wave solutions to KdV-Burgers (KdVB) equation with forcing term. The real part is the sum of the shock wave solution of a Burgers equation and the solitary wave solution of a KdV equation with forcing term, while the imaginary part is the product of a shock wave solution of Burgers with a solitary wave travelling solution of KdV equation. The method gives more solutions than the previous methods.

Abstract

In this paper, we used modified tanh-coth method, combined with Riccati equation and secant hyperbolic ansatz to construct abundantly many real and complex exact travelling wave solutions to KdV-Burgers (KdVB) equation with forcing term. The real part is the sum of the shock wave solution of a Burgers equation and the solitary wave solution of a KdV equation with forcing term, while the imaginary part is the product of a shock wave solution of Burgers with a solitary wave travelling solution of KdV equation. The method gives more solutions than the previous methods.

참고문헌 (34)

  1. R. Abazari, "Application of extended Tanh function method on KdV-Burgers equation with forcing term", Romanian J. Phys, 59(1-2), pp.3~11 (2014)
  2. M. Abdou, "New exact solutions of kdv equation in an elastic tube filled with a variable viscosity fluid", Stud. Nonlinear Sci, 3(2), pp.62~68 (2012)
  3. M. A. Abdou, "Modified extended tanh-function method and its application on nonlinear physical equations", Phys. Lett. A, 353(6), pp.487~492 (2006)
  4. G. Adomian, "Solving frontier problems of physics: the decomposition method", Fundam. Theor. Phys, 60 (1994), Kluwer Academic Publishers Group[DOI]
  5. M. Ali Akbar, "Generalized and improved(G0", G)-expansion method combined with Jacobi elliptic equation, 2014, pp.61(6), 669~676
  6. A. H. A. Ali, "New exact solutions of some nonlinear partial differential equations", Int. J. Nonlinear Sci, 5(1), pp.79~88 (2008)
  7. A. Bekir, "On traveling wave solutions to combined KdV-mKdV equation and modified Burgers-KdV equation", Commun. Nonlinear Sci. Numer. Simul, 14(4), pp.1038~1042 (2009)[DOI]
  8. E. Bilyay, "Extreme waves at filyos, southern black sea", Nat. Hazards Earth Syst. Sci, 11(3), pp.659~666 (2011)
  9. Y. B. Chukkol, "Exact solutions to the KDVBurgers equation with forcing term using Tanh-Coth method", AIP Conf. Proc, 1870(1), pp.040024~ (2017)
  10. M. Dehghan, "The solution of the variable coefficients fourth-order parabolic partial differential equations by the homotopy perturbation method", Z. Naturforsch. A, 64(7–8), pp.420~430 (2009)
  11. M. Dehghan, "Solving nonlinear fractional partial differential equations using the homotopy analysis method", Numer. Methods Partial Differential Equations, 26(2), pp.448~479 (2010)[DOI]
  12. M. Dehghan, "Application of the Exp-function method for solving a partial differential equation arising in biology and population genetics", Internat. J. Numer. Methods Heat Fluid Flow, 21(6-7), pp.736~753 (2011)[DOI]
  13. H. Demiray, "A complex travelling wave solution to the kdv–burgers equation", Phys. Lett. A, 344(6), pp.418~422 (2005)
  14. E. Fan, "Extended tanh-function method and its applications to nonlinear equations", Phys. Lett. A, 277(4-5), pp.212~218 (2000)[DOI]
  15. E. Fan, "Two new applications of the homogeneous balance method", Phys. Lett. A, 265(5-6), pp.353~357 (2000)[DOI]
  16. E. Fan, "Applications of extended tanh method to"special"types of nonlinear equations", Appl. Math. Comput, 141(2-3), pp.351~358 (2003)[DOI]
  17. E. Fan, "A new complex line soliton for the two-dimensional KdV-Burgers equation", Phys. Lett. A, 291(6), pp.376~380 (2001)[DOI]
  18. Z. Feng, "Approximate solution of the Burgers-Korteweg-de Vries equation", Commun. Pure Appl. Anal, 6(2), pp.429~440 (2007)[DOI]
  19. B. Ibis, "Approximate solutions some nonlinear evolutions equations by using the reduced differential transform method", Int. J. Appl. Math. Res, 3(1), pp.288~302 (2012)
  20. H. Jia, "Solitons solutions for some nonlinear evolution equations", Appl. Math. Comput, 217(4), pp.1678~1687 (2010)[DOI]
  21. R. S. Johnson, "A non-linear equation incorporating damping and dispersion", J. Fluid Mech, 42, pp.49~60 (1970)[DOI]
  22. N. A. Kudryashov, "Extended models of non-linear waves in liquid with gas bubbles", Int. J. Non Linear Mech, 63, pp.31~38 (2014)
  23. H. Leblond, "Ultrashort light bullets described by the two-dimensional sine-gordon equation", Phys. Rev. A, 81(6), pp.063815~ (2010)
  24. W. Malfliet, "Solitary wave solutions of nonlinear wave equations", Amer. J. Phys, 60(7), pp.650~654 (1992)[DOI]
  25. Z. Odibat, "A Riccati equation approach and travelling wave solutions for nonlinear evolution equations", Int. J. Appl. Comput. Math, 3(1), pp.1~13 (2017)[DOI]
  26. A. H. Salas S, "Exact solutions for a third-order KdV equation with variable coefficients and forcing term", Math. Probl. Eng., 2009, pp.737928~737940 (2009)[DOI]
  27. A. M. Wazwaz, "The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations", Appl. Math. Comput, 184(2), pp.1002~1014 (2007)[DOI]
  28. A. M. Wazwaz, "Partial differential equations and solitary waves theory, Nonlinear Physical Science" (2009), Higher Education Press
  29. A. M. Wazwaz, "Partial differential equations and solitary waves theory, Nonlinear Physical Science" (2009), Higher Education Press
  30. L. Wazzan, "A modified tanh-coth method for solving the KdV and the KdV-Burgers’equations", Commun. Nonlinear Sci. Numer. Simul, 14(2), pp.443~450 (2009)[DOI]
  31. L. V. Wijngaarden, "On the equations of motion for mixtures of liquid and gas bubbles", J. Fluid Mech, 33(3), pp.465~474 (1968)
  32. N. Zahibo, "Weakly damped KdV soliton dynamics with the random force", Chaos Solitons Fractals, 39(4), pp.1645~1650 (2009)
  33. S. Zhang, "Exp-function method exactly solving the KdV equation with forcing term", Appl. Math. Comput, 197(1), pp.128~134 (2008)[DOI]
  34. S. Zhang, "Soliton solutions and dynamical evolutions of a generalized akns system in the framework of inverse scattering transform", Optik, 137, pp.228~237 (2017)

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