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Nonlinear Dynamics

, Volume 84, Issue 1, pp 135–141 | Cite as

Symmetries and conservation laws of a fifth-order KdV equation with time-dependent coefficients and linear damping

  • R. de la RosaEmail author
  • M. L. Gandarias
  • M. S. Bruzón
Original Paper

Abstract

A fifth-order KdV equation with time-dependent coefficients and linear damping has been studied. Symmetry groups have several different applications in the context of nonlinear differential equations; for instance, they can be used to determine conservation laws. We obtain the symmetries of the model applying Lie’s classical method. The choice of some arbitrary functions of the equation by the equivalence transformation enhances the study of Lie symmetries of the equation. We have determined the subclasses of the equation which are nonlinearly self-adjoint. This allow us to obtain conservation laws by using a theorem proved by Ibragimov which is based on the concept of adjoint equation for nonlinear differential equations.

Keywords

Classical symmetries Equivalence transformations Partial differential equations Conservation laws 

Mathematics Subject Classification

35C07 35Q53 

Notes

Acknowledgments

We would like to thank the Editor and Referees for their timely and valuable comments and suggestions. The authors acknowledge the financial support from Junta de Andalucia group FQM-201. The first author express his sincerest gratitude to the Universidad Politécnica de Cartagena for supporting him. The second and third authors also acknowledge the support of DGICYT Project MTM2009-11875 with the participation of FEDER.

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • R. de la Rosa
    • 1
    Email author
  • M. L. Gandarias
    • 1
  • M. S. Bruzón
    • 1
  1. 1.Department of MathematicsUniversity of CádizCádizSpain

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