An approach is proposed to obtain some exact explicit solutions in terms of elliptic functions to the Novikov-Veselov equation (NVE[V(x, y, t)] = 0). An expansion ansatz V → ψ = Σ2j=0 ajfj is used to reduce the NVE to the ordinary differential equation (f')2 = R(f), where R(f) is a fourth degree polynomial in f. The wellknown solutions of (f')2 = R(f) lead to periodic and solitary wave like solutions V. Subject to certain conditions containing the parameters of the NVE and of the ansatz V → ψ the periodic solutions V can be used as start solutions to apply the (linear) superposition principle proposed by Khare and Sukhatme.
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