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Residual Symmetries and Bäcklund Transformations of Strongly Coupled Boussinesq–Burgers System

School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
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Symmetry 2019, 11(11), 1365; https://doi.org/10.3390/sym11111365
Received: 19 September 2019 / Revised: 22 October 2019 / Accepted: 24 October 2019 / Published: 4 November 2019
In this article, we construct a new strongly coupled Boussinesq–Burgers system taking values in a commutative subalgebra Z 2 . A residual symmetry of the strongly coupled Boussinesq–Burgers system is achieved by a given truncated Painlevé expansion. The residue symmetry with respect to the singularity manifold is a nonlocal symmetry. Then, we introduce a suitable enlarged system to localize the nonlocal residual symmetry. In addition, a Bäcklund transformation is obtained with the help of Lie’s first theorem. Further, the linear superposition of multiple residual symmetries is localized to a Lie point symmetry, and a N-th Bäcklund transformation is also obtained. View Full-Text
Keywords: (2+1)-dimensional strongly coupled Boussinesq–Burgers system; residual symmetry; Bäcklund transformation; Painlevé analysis (2+1)-dimensional strongly coupled Boussinesq–Burgers system; residual symmetry; Bäcklund transformation; Painlevé analysis
MDPI and ACS Style

Wang, H.; Zhang, Y. Residual Symmetries and Bäcklund Transformations of Strongly Coupled Boussinesq–Burgers System. Symmetry 2019, 11, 1365.

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