On hyperbolic and rational solutions of the cubically nonlinear Schr\"odinger equation

TL;DR

This paper expands the set of known non-generic solutions for the cubically nonlinear Schrödinger equation by describing a new family of solutions, building on previous non-existence and solution results.

Contribution

It introduces a new family of solutions that enlarges the set of non-generic solutions for the equation, extending prior work.

Findings

Identified a new family of solutions for the nonlinear Schrödinger equation.

Extended the set of non-generic solutions beyond previous results.

Built upon earlier non-existence proofs to find additional solutions.

Abstract

In a previous article we have proved non-existence of certain "solutions" of the cubically nonlinear Schr\"odinger equation in the general case, and presented solutions in the non-generic case. -- In the present article we describe a further family of solutions enlarging the set of non-generic solutions.