Bilinear structure and determinant solution for the relativistic Lotka–Volterra equation

The relativistic Lotka–Volterra (RLV) lattice and the discrete-time relativistic Lotka–Volterra (dRLV) lattice are investigated by using the bilinear formalism. The bilinear equations for them are systematically constructed with the aid of the singularity confinement test. It is shown that the RLV l...

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Bibliographic Details
Published in:Physics letters. A 2000-05, Vol.270 (3), p.122-131
Main Authors: Maruno, Ken-ichi, Oikawa, Masayuki
Format: Article
Language:English
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Summary:The relativistic Lotka–Volterra (RLV) lattice and the discrete-time relativistic Lotka–Volterra (dRLV) lattice are investigated by using the bilinear formalism. The bilinear equations for them are systematically constructed with the aid of the singularity confinement test. It is shown that the RLV lattice and dRLV lattice are decomposed into the Bäcklund transformations of the Toda lattice system. The N-soliton solutions are explicitly constructed in the form of the Casorati determinant.
ISSN:0375-9601
1873-2429
DOI:10.1016/S0375-9601(00)00176-6