Some elliptic traveling wave solutions to the Novikov-Veselov equation

摘要

An approach is proposed to obtain some exact explicit solutions in terms of elliptic functions to the Novikov-Veselov equation (NVE[ψ(x, y, t)] = 0). An expansion ansatz ψ → g = Σj=02ajfjis 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 ψ. Subject to certain conditions containing the parameters of the NVE and of the ansatz ψ → g the periodic solutions ψ can be used as start solutions to apply the (linear) superposition principle proposed by Khare and Sukhatme.