Anderson Hamiltonian and associated Nonlinear Stochastic Wave and Schr\"odinger equations in the full space

TL;DR

This paper investigates the Anderson Hamiltonian in the full space and establishes well-posedness results for nonlinear stochastic wave and Schrödinger equations with polynomial nonlinearities.

Contribution

It provides the first comprehensive analysis of the Anderson Hamiltonian in the full space and proves well-posedness for associated nonlinear stochastic PDEs.

Findings

Proved well-posedness of nonlinear stochastic wave equations.

Established well-posedness of nonlinear Schrödinger equations.

Analyzed the Anderson Hamiltonian in the full space setting.

Abstract

In this article, we study the Anderson Hamiltonian in the full space and prove wellposedness of nonlinear stochastic wave equation and NLS with polynomial nonlinearities.