Special Solutions of Bi-Riccati Delay-Differential Equations

Abstract

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.

References in corpus (2)

• On integration of the closed KdV dressing chain
• On some new forms of lattice integrable equations

Cited by in corpus (3)

• Singularity confinement in delay-differential Painlevé equations
• A systematic construction of integrable delay-difference and delay-differential analogues of soliton equations
• Integrable delay-difference and delay-differential analogues of the KdV, Boussinesq, and KP equations