Symmetry Reductions, Exact Solutions and Conservation Laws of Asymmetric Nizhnik-Novikov-Veselov Equation

By applying a direct symmetry method, we get the symmetry of the asymmetric Nizhnik-Novikov-Veselov equation (ANNV).Taking the special case, we have a finite-dimensional symmetry. Byusing the equivalent vector of the symmetry, we construct aneight-dimensional symmetry algebra and get the optimal system ofgroup-invariant solutions. To every case of the optimal system, wereduce the ANNV equation and obtain some solutions to the reducedequations. Furthermore, we find some new explicit solutions of theANNV equation. At last, we give the conservation laws of the ANNV equation.