Numerical computation of solutions of the critical nonlinear Schrodinger equation after the singularity

TL;DR

This paper develops a numerical method using the Mori-Zwanzig formalism to compute solutions of the 1D critical nonlinear Schrödinger equation beyond singularity formation, aligning with recent theoretical findings.

Contribution

It introduces a reduced model for post-singularity solutions of the 1D critical nonlinear Schrödinger equation, enabling numerical exploration of solutions after singularity.

Findings

Post-singularity solutions match characteristics of recent theoretical models

The Mori-Zwanzig formalism effectively captures solution behavior after singularity

Numerical results confirm the feasibility of studying singularity aftermaths

Abstract

We present numerical results for the solution of the 1D critical nonlinear Schrodinger with periodic boundary conditions and initial data that give rise to a finite time singularity. We construct, through the Mori-Zwanzig formalism, a reduced model which allows us to follow the solution after the formation of the singularity. The computed post-singularity solution exhibits the same characteristics as the post-singularity solutions constructed recently by Terence Tao.