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Potential systems of a Buckley–Leverett equation: Lie point symmetries and conservation laws

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Abstract

In this work, we study a Buckley–Leverett equation of two-phase flow in porous media from the point of view of the Lie theory. We find that for some functions the equation has abundant exact solutions expressible in terms of Jacobi elliptic functions and consequently has many solutions in the form of periodic waves or solitary waves. We determine low-order conservation laws by using the multiplier method. From conservations laws, we construct the potential systems. From these systems we deduce potential equations. We study these equations from the point of view of Lie theory. Moreover, for these equations some nontrivial conservation laws are constructed by using the multipliers method.

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Acknowledgements

We appreciate funds sources to the Plan Propio de Investigación de la Universidad de Cádiz.

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Authors and Affiliations

  1. Department of Mathematics, Universidad de Cádiz, 11510, Cádiz, Spain

    M. S. Bruzón, A. P. Márquez, E. Recio, T. M. Garrido & R. de la Rosa

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  1. M. S. Bruzón
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  2. A. P. Márquez
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  3. E. Recio
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  4. T. M. Garrido
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  5. R. de la Rosa
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Correspondence to M. S. Bruzón.

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Bruzón, M.S., Márquez, A.P., Recio, E. et al. Potential systems of a Buckley–Leverett equation: Lie point symmetries and conservation laws. J Math Chem 58, 831–840 (2020). https://doi.org/10.1007/s10910-020-01110-9

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  • DOI: https://doi.org/10.1007/s10910-020-01110-9

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