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

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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.

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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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Authors and Affiliations

  1. Department of Mathematics, University of Cádiz, Cádiz, Spain

    R. de la Rosa, M. L. Gandarias & M. S. Bruzón

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  1. R. de la Rosa
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  2. M. L. Gandarias
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  3. M. S. Bruzón
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Correspondence to R. de la Rosa.

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de la Rosa, R., Gandarias, M.L. & Bruzón, M.S. Symmetries and conservation laws of a fifth-order KdV equation with time-dependent coefficients and linear damping. Nonlinear Dyn 84, 135–141 (2016). https://doi.org/10.1007/s11071-015-2254-3

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  • DOI: https://doi.org/10.1007/s11071-015-2254-3

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