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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 odes involved in description of the invariant solutions are… Click to show full abstract
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 $$N \ge 3$$ N ≥ 3 with respect to the spatial variables. Finally we compute all conservation laws that are associated to cosymmetries of second order.
Journal Title: Analysis and Mathematical Physics
Year Published: 2021
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