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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


One Kink Solution for a Variety of Nonlinear Fifth-order Equations

Discontinuity, Nonlinearity, and Complexity 1(2) (2012) 161--170 | DOI:10.5890/DNC.2012.05.001

Abdul-MajidWazwaz

Department of Mathematics, Saint Xavier University, Chicago, IL 60655, USA

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Abstract

In this work, we derive one kink solution for each equation of a variety of nonlinear fifth-order equations. Each equation involves a third order temporal derivative and a mixed fifth-order derivative. The simplified form of Hirota’s method will be used to derive these solutions. The proposed work presents reliable approach compared to some existing techniques.

References

  1. [1]  Wazwaz, A.M. (2011), A new fifth-order nonlinear integrable equation: multiple soliton solutions,Phys. Scr., 83, 015012.
  2. [2]  Wazwaz, A.M. (2011), A new generalized fifth-order nonlinear integrable equation,Phys. Scr., 83, 035003.
  3. [3]  Hirota, R. (2004), The Direct Method in Soliton Theory, Cambridge University Press, Cambridge.
  4. [4]  Hereman,W. and Nuseir, A. (1997), Symbolic methods to construct exact solutions of nonlinear partial differential equations, Mathematics and Computers in Simulation, 43, 13-27.
  5. [5]  Hereman,W. (2006), Symbolic Computation of Conservation Laws of Nonlinear Partial Differential Equations in Multi-dimensions,International Journal of Quantum Chemistry, 106 (1), 278-299.
  6. [6]  Triki, H., Wazwaz, A.M. (2009), Sub-ODE method and soliton solutions for the variable- coefficient mKdV equation, Appl. Math. Comput., 214, 370-373.
  7. [7]  Triki, H., Wazwaz, A.M. (2009), Bright and dark soliton solutions for a K(m,n) equation with t-dependent coefficients, Phys. Lett A, 373, 2162-2215.
  8. [8]  Dehghan, M. and Shokri, A.(2008),A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions,Comput.Math. Simulation, 79, 700-715.
  9. [9]  Dehghan, M. and Ghesmati, A.(2010), Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM), Comput. Phys. Commun., 181, 772-786.
  10. [10]  Wazwaz, A.M. (2009), Partial Differential Equations and Solitary Waves Theorem, Springer and HEP, Berlin and Beijing.
  11. [11]  Wazwaz, A.M. (2010), Multiple soliton solutions for coupled KdV and coupled KP Systems, Canadian Journal of Physics, 87( 12), 1227-1232 .
  12. [12]  Wazwaz, A.M. (2010), Multiple soliton solutions for the (2+1)-dimensional asymmetric Nizhanik-Novikov- Veselov equation, Nonlinear Analysis Series A: Theory, Methods & Applications, 72, 1314-1318.
  13. [13]  Wazwaz, A.M. (2010), The (2+1) and (3+1)-dimensional CBS equation: multiple soliton solutions and multiple singular soliton solutions, Multiple, Zeitschrift fur Naturforschung A (ZNA), 65a, 173-181.
  14. [14]  Wazwaz, A.M. (2007),Multiple-front solutions for the Burgers equation and the coupled Burgers equations, Appl. Math. Comput., 190, 1198-1206.
  15. [15]  Wazwaz, A.M. (2007), New solitons and kink solutions for the Gardner equation, Communications in Nonlinear Science and Numerical Simulation, 12(8), 1395-1404.
  16. [16]  Wazwaz, A.M. (2007), Multiple-soliton solutions for the Boussinesq equation, Appl. Math. Comput., 192, 479- 486.
  17. [17]  Wazwaz, A.M. (2008), The Hirota's direct method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera-Ito seventh-order equation,Appl.Math. Comput., 199(1), 133-138.
  18. [18]  Wazwaz, A.M. (2008), The Hirota's direct method for multiple-soliton solutions for three model equations of shallow water waves, Appl. Math. Comput., 201(1/2), 489-503.
  19. [19]  Wazwaz, A.M. (2008), Solitons and singular solitons for the Gardner-KP equation, Appl. Math. Comput., 204(1), 162-169.
  20. [20]  Wazwaz, A.M. (2009),Multiple kink solutions and multiple singular kink solutions for (2+1)-dimensional nonlinear models generated by the Jaulent-Miodek hierarchy, Phys. Lett. A, 373, 1844-1846.