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Incompressible fluids are of current interest. Considering a (3+1)-dimensional variable-coefficient Boiti–Leon–Manna–Pempinelli model for an incompressible fluid, we perform symbolic computation to work out a variable-coefficient-dependent auto-Bäcklund transformation, along with two variable-coefficient-dependent classes of the shock-wave-type solutions. Our auto-Bäcklund transformation is different from the recently reported bilinear one.

Incompressible-Fluid Symbolic Computation and Bäcklund Transformation: (3+1)-Dimensional Variable-Coefficient Boiti–Leon–Manna–Pempinelli Model