2006-05-20["PIER_181_24111001.png","PIER_182_25012003.png","PIER_183_25052305.png","other\/special_issue_13.png"]
Some Elliptic Traveling Wave Solutions to the Novikov-Veselov Equation
By Julia Nickel
V. Serov
H. Schurmann
Progress In Electromagnetics Research, Vol. 61, 323-331, 2006
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 → 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.