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We study symmetries, invariant solutions, and conservation laws for the dispersionless Veselov–Novikov equation. The emphasis is placed on cases when the  ode s involved in description of the invariant solutions are integrable by quadratures. Then we find some non-invariant solutions, in particular, solutions that are polynomials of an arbitrary degree    $$N \ge 3$$  N ≥ 3 with respect to the spatial variables. Finally we compute all conservation laws that are associated to cosymmetries of second order.

The dispersionless Veselov–Novikov equation: symmetries, exact solutions, and conservation laws