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Conservation laws and symmetry analysis for a quasi-linear strongly-damped wave equation

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Abstract

In this paper, it is considered a quasi-linear strongly-damped wave equation defined by a non-linear partial differential equation of third order. The equation describes motions of viscoelastic solids. We study the conservation laws of this equation. By applying the multiplier method of Anco and Bluman to the equation, we find the multipliers. Consequently, we obtain a complete classification of conservation laws. Moreover, we use the Lie-group theory to analyse the symmetries of the equation. From the Lie symmetries, all the reductions are determined. Afterwards, we construct exact solutions with physical interest: travelling wave solutions.

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Acknowledgements

A. P. Márquez expresses its sincere gratitude to the Plan Propio de Investigación y Transferencia of the University of Cadiz. The authors express their sincere gratitude to the financial support of Junta de Andalucía FQM-201 group.

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  1. Department of Mathematics, Facultad de Ciencias Campus del Río San Pedro, University of Cadiz, 11510, Puerto Real, Spain

    Almudena del Pilar Márquez & María de los Santos Bruzón

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  1. Almudena del Pilar Márquez
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  2. María de los Santos Bruzón
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Correspondence to Almudena del Pilar Márquez.

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del Pilar Márquez, A., de los Santos Bruzón, M. Conservation laws and symmetry analysis for a quasi-linear strongly-damped wave equation. J Math Chem 58, 1489–1498 (2020). https://doi.org/10.1007/s10910-020-01146-x

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