Physics of Wave Phenomena

, Volume 19, Issue 1, pp 24–29

Bright and dark solitons of the Rosenau-Kawahara equation with power law nonlinearity

Solitons and Chaos

Abstract

In this paper, the topological (dark) as well as non-topological (bright) soliton solutions to the Rosenau-Kawahara equation with power law nonlinearity are obtained by the solitary wave ansatz method. A couple of conserved quantities are also calculated for the case of bright soliton solution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Biswas and H. Triki, “1-Soliton Solution of the Klein-Gordon-Schrödinger’s Equation with Power Law Nonlinearity,” Appl. Math. Comp. 217(8), 3869 (2010).MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    J. Cai, S. Xie, and C. Yang, “Two Loop Soliton Solutions to the Reduced Ostrovsky Equation,” Int.Math. Forum. 3(31), 1529 (2008).MathSciNetMATHGoogle Scholar
  3. 3.
    N. A. Kudryashov and N.B. Loguinova, “Be Careful with Exp-Function Method,” Commun. Nonlinear Sci. Numerical Simulation. 14(5), 1881 (2009).MathSciNetADSCrossRefMATHGoogle Scholar
  4. 4.
    N. A. Kudryashov, “Seven Common Errors in Finding Exact Solutions of Nonlinear Differential Equations,” Commun. Nonlinear Sci. Numerical Simulation. 14(9–10), 3507 (2009)MathSciNetADSCrossRefMATHGoogle Scholar
  5. 5.
    M. Labidi and K. Omrani, “Numerical Simulation of the Modified Regularized Long Wave Equation by He’s Variational Iteration Method,” Numerical Methods for Partial Differential Equations (doi: 10.1002/num.20537).Google Scholar
  6. 6.
    A. C. J. Luo and C. A. Tan, “Resonant and Stationary Waves in Rotating Disks,” Nonlinear Dynam. 24(4), 359 (2004).CrossRefGoogle Scholar
  7. 7.
    A. C. J. Luo and B. C. Gegg, “An Analytical Prediction of Sliding Motions along Discontinuous Boundary in Non-Smooth Dynamical System,” Nonlinear Dynam. 49(3), 401 (2007).MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    A.-M. Wazwaz, “Multiple-Soliton Solutions for the KP Equation by Hirota’s Bilinear Method and by the Tanh-Coth Method,” Appl. Math. Comp. 190(1), 633 (2007).MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    A.-M. Wazwaz, “Regular Soliton Solutions and Singular Soliton Solutions for the Modified Kadomtsev-Petviashvili Equations,” Appl. Math. Comp. 204(1), 227 (2008).MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    J.-M. Zuo, “Solitons and Periodic Solutions for the Rosenau-KdV and Rosenau-Kawahara Equation,” Appl.Math. Comp. 215(2), 835 (2009).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Allerton Press, Inc. 2011

Authors and Affiliations

  1. 1.Department of Mathematical Sciences, Center for Research and Education in Optical Sciences and ApplicationsDelaware State UniversityDoverUSA
  2. 2.Radiation Physics Laboratory, Department of Physics, Faculty of SciencesBadji Mokhtar UniversityAnnabaAlgeria
  3. 3.Ecole Polytechnique de TunisieLa MarsaTunisia

Personalised recommendations