SOME ELLIPTIC TRAVELING WAVE SOLUTIONS TO THE NOVIKOV-VESELOV EQUATION

Abstract

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 = 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 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 the periodic solutions V can be used as start solutions to apply the (linear) superposition principle proposed by Khare and Sukhatme.