Find in Library

In this article, we construct a new strongly coupled Boussinesq&#8722;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&#8722;Burgers system is achieved by a given truncated Painlev&#233; 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 B&#228;cklund transformation is obtained with the help of Lie&#8217;s first theorem. Further, the linear superposition of multiple residual symmetries is localized to a Lie point symmetry, and a <i>N</i>-th B&#228;cklund transformation is also obtained.