Abstract
The symmetry of the (3 + 1)-dimensional partial differential equation has been derived via a direct symmetry method and proved to be infinite dimensional non-Virasoro type symmetry algebra. Many kinds of symmetry reductions have been obtained, including the (2 + 1)-dimensional ANNV equation and breaking soliton equation. And some new soliton solutions and complex solutions are obtained due to the Riccati equation method and symbolic computation.
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