Absence of solitons for the defocusing NLS equation on the half-line

TL;DR

This paper proves the long-standing conjecture that the defocusing nonlinear Schrödinger equation on the half-line does not support soliton solutions, clarifying the behavior of this integrable system in boundary conditions.

Contribution

The paper provides a rigorous proof confirming the absence of solitons for the defocusing NLS equation on the half-line, resolving a key conjecture in the field.

Findings

Confirmed the non-existence of solitons in the defocusing NLS on the half-line

Resolved a long-standing conjecture in integrable systems

Clarified the boundary behavior of the defocusing NLS equation

Abstract

It has been conjectured that the defocusing nonlinear Schr\"odinger (NLS) equation on the half-line does not admit solitons. We give a proof of this conjecture.