Properties of the solitonic potentials of the heat operator

TL;DR

This paper investigates the detailed properties and asymptotic behavior of solitonic potentials related to the heat operator, focusing on their ray structure in the parameter space.

Contribution

It provides a detailed analysis of the asymptotic behavior and ray structure of solitonic potentials for the heat equation, enhancing understanding of their mathematical properties.

Findings

Asymptotic behavior of solitonic potentials characterized

Ray structure of potentials identified on the x-plane

Dependence of behavior on potential parameters clarified

Abstract

Properties of the pure solitonic $\tau$-function and potential of the heat equation are studied in detail. We describe the asymptotic behavior of the potential and identify the ray structure of this asymptotic behavior on the $x$-plane in dependence on the parameters of the potential.