We study symmetries, invariant solutions, and conservation laws for the dispersionless Veselov–Novikov equation. The emphasis is placed on cases when the odes 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 \(N \ge 3\) with respect to the spatial variables. Finally we compute all conservation laws that are associated to cosymmetries of second order.

中文翻译：

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无色散 Veselov-Novikov 方程：对称性、精确解和守恒定律

我们研究无色散 Veselov-Novikov 方程的对称性、不变解和守恒定律。重点放在描述不变解所涉及的ode可通过正交积分的情况。然后我们找到一些非不变解，特别是关于空间变量的任意次数\(N\ge 3\)多项式的解。最后，我们计算所有与二阶共对称相关的守恒定律。