QUANTUM SOLITONS

Abstract

Two themes are considered in this paper. First of all in the Introduction a comment is made about the Tzitzéica equation which occurred in the author's work as reported in [1]. Much recent work has referred to this equation and a representative bibliography is given in this paper with brief comments. The second theme of this paper is concerned with work surrounding Quantum Solitons and the author's talk at the ISLAND 2 meeting under the title ‘Quantum solitons’ is briefly summarised. An extended review of this subject matter has now appeared in [2] and as there the quantum soliton of the quantum attractive NLS model is seen as a ‘qubit’ for quantum information purposes. It is hoped that this summary and/or the reference [2] can help to stimulate further interest in this ‘quantum’ aspect of our subject in the solitons community. The actual observation of a quantum soliton is also reported and a proper theoretical description of it given. Reference is made to $q$-boson lattices first as a simple example of the quantum inverse method in the Introduction and then as a subject matter in its own right at the end of the paper.