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arXiv · 2103.08734

Point-symmetry pseudogroup, Lie reductions and exact solutions of Boiti-Leon-Pempinelli system

Diana S. Maltseva·Roman O. Popovych
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Abstract

We carry out extended symmetry analysis of the (1+2)-dimensional Boiti-Leon-Pempinelli system, which corrects, enhances and generalizes many results existing in the literature. The point-symmetry pseudogroup of this system is computed using an original megaideal-based version of the algebraic method. A number of meticulously selected differential constraints allow us to construct families of exact solutions of this system, which are significantly larger than all known ones. After classifying one- and two-dimensional subalgebras of the entire (infinite-dimensional) maximal Lie invariance algebra of this system, we study only its essential Lie reductions, which give solutions beyond the above solution families. Among reductions of the Boiti-Leon-Pempinelli system using differential constraints or Lie symmetries, we identify a number of famous partial and ordinary differential equations. We also show how all the constructed solution families can significantly be extended by Laplace and Darboux transformations.

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Diana S. Maltseva, Roman O. Popovych. 2021-03-15. Point-symmetry pseudogroup, Lie reductions and exact solutions of Boiti-Leon-Pempinelli system. https://doi.org/10.1016/j.physd.2024.134081

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