Year: 2022
Type: preprint
Abstract: We investigate singularly perturbed nonlinear complex differential systems of the form $\hbar \partial_x f = F (x, \hbar, f)$ where $\hbar$ is a small complex perturbation parameter. Under a geometric assumption on the eigenvalues of the Jacobian matrix of $F$, we prove an Existence and Uniqueness Theorem for exact perturbative solutions; i.e., holomorphic solutions with prescribed perturbative expansions in $\hbar$. In fact, these solutions are the Borel resummation of the formal perturbative solutions.
Source: arXiv (Cornell University)
Author: Nikolaev, Nikita
Institutions: University of Birmingham, University of Sheffield
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4293306122