On alleged solutions of the cubically nonlinear Schr\"odinger equation

TL;DR

This paper critically examines a common solution approach for the cubically nonlinear Schrödinger equation, providing numerical evidence that questions its validity based on analytical insights.

Contribution

It demonstrates through numerical examples that a widely used ansatz for the equation is inconsistent, challenging existing solution methods.

Findings

Numerical example shows inconsistency of the ansatz.

Analytical results support the numerical findings.

Questions the validity of common solution approaches.

Abstract

On the basis of analytical results, we present a numerical example that indicates inconsistency of a widely used ansatz with cubically nonlinear Schr\"odinger equation.