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Some Elliptic Traveling Wave Solutions to the Novikov-Veselov Equation

By Julia Nickel, V. Serov, and H. Schurmann
Progress In Electromagnetics Research, Vol. 61, 323-331, 2006


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.


Julia Nickel, V. Serov, and H. Schurmann, "Some Elliptic Traveling Wave Solutions to the Novikov-Veselov Equation," Progress In Electromagnetics Research, Vol. 61, 323-331, 2006.


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