Equation with the lower negative time number in the Davey--Stewartson hierarchy

TL;DR

This paper extends the Davey--Stewartson hierarchy by constructing an integrable equation with a lower negative time variable, revealing new integrable systems in 1+1 dimensions.

Contribution

It introduces a novel integrable equation with a negative time variable in the hierarchy, expanding the understanding of the Davey--Stewartson systems.

Findings

Constructed an integrable equation with lower negative time variable.

Reduced system yields a new 1+1 dimensional integrable equation.

Extended the hierarchy approach to include negative time variables.

Abstract

In \textit{SIGMA} \textbf{17} (2021), 091, 12 p.p.\ we have presented an integrable system with a negative time variable number for the Davey-Stewartson hierarchy. Here we develop this approach to construct an integrable equation with a lower time variable number. In addition, we show that the system reduced by this time is a new integrable equation in the dimension $1+1$.