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Residual Symmetries and Bäcklund Transformations of Strongly Coupled Boussinesq–Burgers System
oleh: Haifeng Wang, Yufeng Zhang
Format: | Article |
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Diterbitkan: | MDPI AG 2019-11-01 |
Deskripsi
In this article, we construct a new strongly coupled Boussinesq−Burgers system taking values in a commutative subalgebra <inline-formula> <math display="inline"> <semantics> <msub> <mi>Z</mi> <mn>2</mn> </msub> </semantics> </math> </inline-formula>. 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 <i>N</i>-th Bäcklund transformation is also obtained.