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Solitary wave solution for KdV equation with power-law nonlinearity and time-dependent coefficients

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Abstract

This paper obtains an exact solitary wave solution of the Korteweg–de Vries equation with power law nonlinearity with time-dependent coefficients of the nonlinear as well as the dispersion terms. In addition, there are time-dependent damping and dispersion terms. The solitary wave ansatz is used to carry out the analysis. It is only necessary for the time-dependent coefficients to be Riemann integrable. As an example, the solution of the special case of cylindrical KdV equation falls out.

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References

  1. Antonova, M., Biswas, A.: Adiabatic parameter dynamics of perturbed solitary waves. Commun. Nonlinear Sci. Numer. Simul. 14(3), 734–748 (2009)

    Article  MathSciNet  Google Scholar 

  2. Biswas, A.: Solitary wave solution for the generalized KdV equation with time-dependent damping and dispersion. Commun. Nonlinear Sci. Numer. Simul. (to appear)

  3. Johnson, R.S.: A Modern Introduction to the Mathematical Theory of Water Waves. Cambridge University Press, Cambridge (1997)

    MATH  Google Scholar 

  4. Mayil Vaganan, B., Kumaran, M.S.: Exact linearization and invariant solutions of the generalized Burger’s equation with linear damping and variable viscosity. Stud. Appl. Math. 117, 95–108 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  5. Senthilkumaran, M., Pandiaraja, D., Mayil Vaganan, B.: New explicit solutions of the generalized KdV equations. Appl. Math. Comput. 202(2), 693–699 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. Taogetusang, Sirendaoreji: The Jacobi elliptic function-like exact solutions to two kinds of KdV equations with variable coefficients and KdV equation with forcible term. Chin. Phys. 15, 2809–2818 (2006)

    Article  Google Scholar 

  7. Xiao-Yan, T., Fei, H., Sen-Yue, L.: Variable coefficient KdV equation and the analytical diagnosis of a dipole blocking life cycle. Chin. Phys. Lett. 23, 887–890 (2006)

    Article  Google Scholar 

  8. Xu, X.-G., Meng, X.-H., Gao, Y.-T., Wen, X.-Y.: Analytic N-solitary-wave solution of a variable-coefficient Gardner equation from fluid dynamics and plasma physics. Appl. Math. Comput. (to appear)

  9. Zhang, S.: Exact solution of a KdV equation with variable coefficients via exp-function method. Nonlinear Dyn. 52(1–2), 11–17 (2007)

    Google Scholar 

  10. Zhang, Y., Li, J., Lv, Y.-N.: The exact solution and integrable properties to the variable-coefficient modified Korteweg–de Vries equation. Ann. Phys. 323(12), 3059–3064 (2008)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Center for Research and Education in Optical Sciences and Applications, Department of Applied Mathematics and Theoretical Physics, Delaware State University, Dover, DE, 19901-2277, USA

    Anjan Biswas

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  1. Anjan Biswas
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Correspondence to Anjan Biswas.

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Biswas, A. Solitary wave solution for KdV equation with power-law nonlinearity and time-dependent coefficients. Nonlinear Dyn 58, 345–348 (2009). https://doi.org/10.1007/s11071-009-9480-5

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  • DOI: https://doi.org/10.1007/s11071-009-9480-5

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