## 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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