Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 020, 9 pages      arXiv:1710.06091
Contribution to the Special Issue on Symmetries and Integrability of Difference Equations

Special Solutions of Bi-Riccati Delay-Differential Equations

Bjorn K. Berntson
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK

Received May 15, 2017, in final form March 02, 2018; Published online March 09, 2018

Delay-differential equations are functional differential equations that involve shifts and derivatives with respect to a single independent variable. Some integrability candidates in this class have been identified by various means. For three of these equations we consider their elliptic and soliton-type solutions. Using Hirota's bilinear method, we find that two of our equations possess three-soliton-type solutions.

Key words: delay-differential equations; elliptic solutions; solitons.

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