Type-II hidden symmetry and nonlinear self-adjointness of Boiti–Leon–Pempinelli equation

• Convert BLP equation to (1+1)-dimensional partial differential equation via similarity transformation.
• Analyze hidden symmetry of BLP equations via studying classical and nonclassical symmetries of the (1+1)-dimensional equations.
• Some new invariant solutions of BLP equations are constructed.

This paper focuses on two aspects. Firstly, we convert Boiti–Leon–Pempinelli (BLP) equation to (1+1)-dimensional partial differential equation via similarity transformation, and then analyze hidden symmetry of BLP equations via studying classical and nonclassical symmetries of the (1+1)-dimensional equations. As a byproduct, some new invariant solutions of BLP equations are constructed. Secondly, we show that BLP equation is nonlinearly self-adjoint and give the general formula of conservation laws.