NLS-type equations from quadratic pencil of Lax operators: Negative flows

We formulate and study an integrable model of Nonlinear Schrodinger (NLS)-type through its Lax representation, where one of the Lax operators is quadratic and the other has a rational dependence on the spectral parameter. We discuss the associated spectral problem, the Riemann-Hilbert problem formulation, the conserved quantities, as well as a generalisation for symmetric spaces. In addition we explore the possibilities for modelling with higher order NLS (HNLS) integrable equations and in particular, the relevance of the proposed system. (c) 2022 The Author. Published by Elsevier Ltd. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).

Automated summary

In this paper, an integrable model of Nonlinear Schrodinger (NLS)-type is studied through its Lax representation. The associated spectral problem, the Riemann-Hilbert problem formulation, the conserved quantities, as well as a generalisation for symmetric spaces are discussed. Furthermore, the potential for modeling with higher order NLS (HNLS) integrable equations and the relevance of the proposed system are explored.