Abstract
Ibragimov introduced the concept of nonlinear self-adjoint equations. This definition generalizes the concept of self-adjoint and quasi-self-adjoint equations. Gandarias defined the concept of weak self-adjoint. In this paper, we found a class of nonlinear self-adjoint nonlinear reaction-diffusion-convection equations which are neither self-adjoint nor quasi-self-adjoint nor weak self-adjoint. From a general theorem on conservation laws proved by Ibragimov we obtain conservation laws for these equations.
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Acknowledgements
The authors acknowledge the financial support from Junta de Andalucía group FQM–201 and from project MTM2009-11875. We warmly thank the referees for reading carefully the manuscript and for giving their suggestions.
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Bruzón, M.S., Gandarias, M.L., de la Rosa, R. (2014). Conservation Laws of a Family of Reaction-Diffusion-Convection Equations. In: Carretero-González, R., Cuevas-Maraver, J., Frantzeskakis, D., Karachalios, N., Kevrekidis, P., Palmero-Acebedo, F. (eds) Localized Excitations in Nonlinear Complex Systems. Nonlinear Systems and Complexity, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-02057-0_21
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DOI: https://doi.org/10.1007/978-3-319-02057-0_21
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