Some elliptic traveling wave solutions to the Novikov-Veselov equation

Autor(en): Nickel, J.
Serov, V. S.
Schuermann, H. W.
Stichwörter: CYCLIC IDENTITIES; Engineering; Engineering, Electrical & Electronic; EVOLUTIONAL EQUATIONS; Physics; Physics, Applied; Telecommunications
Erscheinungsdatum: 2006
Herausgeber: E M W PUBLISHING
Journal: PROGRESS IN ELECTROMAGNETICS RESEARCH-PIER
Volumen: 61
Startseite: 323
Seitenende: 331
Zusammenfassung: 
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 -> psi = 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 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.
ISSN: 15598985
DOI: 10.2528/PIER06041202

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