Year: 2024
Type: article
Abstract: The discrete nonlinear Schrödinger equation on $${\mathbb Z}^d$$ Z d , $$d \ge 1$$ d ≥ 1 is an example of a dispersive nonlinear wave system. Being a Hamiltonian system that conserves also the $$\ell ^2({\mathbb Z}^d)$$ ℓ 2 ( Z d ) -norm, the well-posedness of the corresponding Cauchy problem follows for square-summable initial data. In this paper, we prove that the well-posedness continues to hold for initial data that can grow towards infinity, namely anything that has at most a certain power law growth far away from the origin. The growth condition is loose enough to guarantee that, at least in dimension $$d=1$$ d = 1 , initial data sampled from any reasonable equilibrium distribution of the defocusing DNLS satisfies it almost surely.
Source: Journal of Statistical Physics
Author: Aleksis Vuoksenmaa
Institution: University of Helsinki
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W4404716467