Meromorphic Solutions to a Differential--Difference Equation Describing Certain Self-Similar Potentials

TL;DR

This paper proves the existence of meromorphic solutions to a nonlinear differential-difference equation that models self-similar potentials in the Schrödinger operator, advancing understanding of these mathematical structures.

Contribution

It establishes the existence of meromorphic solutions for a specific differential-difference equation related to self-similar Schrödinger potentials, a novel result in the field.

Findings

Existence of meromorphic solutions proven

Application to self-similar Schrödinger potentials demonstrated

Mathematical framework for these solutions developed

Abstract

In this paper we prove the existence of meromorphic solutions to a nonlinear differential difference equation that describe certain self-similar potentials for the Schroedinger operator.