Special Solutions of Bi-Riccati Delay-Differential Equations

TL;DR

This paper investigates special solutions of certain bi-Riccati delay-differential equations, demonstrating the existence of elliptic and soliton-type solutions, including three-soliton solutions for some cases using Hirota's method.

Contribution

It introduces new elliptic and soliton solutions for specific integrability candidates within delay-differential equations, applying Hirota's bilinear method.

Findings

Two equations admit three-soliton solutions.

Elliptic solutions are identified for three equations.

The methods confirm integrability candidates through explicit solutions.

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.