Extended resolvent of heat operator with multisoliton potential

TL;DR

This paper derives the extended resolvent for the heat operator with multisoliton potential, analyzes its properties, and introduces Green's functions to understand their behavior and discontinuities.

Contribution

It provides a novel explicit derivation of the extended resolvent for the heat operator with multisoliton potential and studies its boundedness and discontinuities.

Findings

Extended resolvent explicitly derived for multisoliton heat operator

Boundedness properties established in all variables

Green's functions characterized and their discontinuities analyzed

Abstract

The heat operator with a general multisoliton potential is considered and its extended resolvent, depending on a parameter $q\in\R^2$ is derived. Its boundedness properties in all variables and its discontinuities in the parameter $q$ are given. As the result, the Green's functions are introduced and their properties are studied in detail.