Probabilistic methods for discrete nonlinear Schr\"odinger equations

TL;DR

This paper demonstrates that the thermodynamics of the focusing cubic discrete nonlinear Schrödinger equation are exactly solvable in three or more dimensions, providing explicit formulas for key properties.

Contribution

It introduces an exact solution framework for the thermodynamics of the focusing cubic discrete nonlinear Schrödinger equation in higher dimensions.

Findings

Exact thermodynamic solutions in dimensions three and higher.

Derivation of explicit formulas for thermodynamic quantities.

Advancement in understanding nonlinear Schrödinger equations.

Abstract

We show that the thermodynamics of the focusing cubic discrete nonlinear Schrodinger equation are exactly solvable in dimensions three and higher. A number of explicit formulas are derived.