Some elliptic traveling wave solutions to the Novikov-Veselov equation

An approach is proposed to obtain some ex art explicit solutions in terms of elliptic functions to the Novikov-Veselov equation (NTVE[psi(x,y,t)] = 0). An expansion ansatz psi rarr g = Sigma 2 j=0 a j f j 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 well-known solutions of (f) 2 = R(f) lead to periodic and solitary wave like solutions psi. Subject, to certain conditions containing the parameters of the NVE and of the ansatz psi rarr g the periodic solutions psi can be used as start solutions to apply the (linear) superposition principle proposed by Khare and Sukhatme