Extended resolvent of heat operator with multisoliton potential

Abstract

The heat operator with a general multisoliton potential is considered and its extended resolvent, depending on a parameter $q\in {\mathbb{R}}^2$ 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.

arXiv admin note: text overlap with arXiv:1201.0152

References in corpus (4)

• KP solitons in shallow water
• On the equivalence of different approaches for generating multisoliton solutions of the KPII equation
• Building extended resolvent of heat operator via twisting transformations
• Heat operator with pure soliton potential: properties of Jost and dual Jost solutions

Cited by in corpus (2)

• Hirota difference equation: IST, Darboux transformation and solitons
• The direct scattering problem for the perturbed $\text{Gr}(1,2{)}_{\ge 0}$ Kadomtsev-Petviashvili solitons