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

Rossen I. Ivanov

doi:10.1016/j.chaos.2022.112299

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

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Abstract

We formulate and study an integrable model of Nonlinear Schrödinger (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.

Original language	English
Article number	112299
Journal	Chaos, Solitons and Fractals
Volume	161
DOIs	https://doi.org/10.1016/j.chaos.2022.112299
Publication status	Published - Aug 2022

Keywords

Bi-Hamiltonian integrable systems
Derivative nonlinear Schrödinger equation
Hermitian symmetric spaces
Nonlocal integrable equations
Simple Lie algebra

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10.1016/j.chaos.2022.112299Licence: CC BY

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title = "NLS-type equations from quadratic pencil of Lax operators: Negative flows",

abstract = "We formulate and study an integrable model of Nonlinear Schr{\"o}dinger (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.",

keywords = "Bi-Hamiltonian integrable systems, Derivative nonlinear Schr{\"o}dinger equation, Hermitian symmetric spaces, Nonlocal integrable equations, Simple Lie algebra",

author = "Ivanov, \{Rossen I.\}",

note = "Publisher Copyright: {\textcopyright} 2022 The Author",

year = "2022",

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language = "English",

volume = "161",

journal = "Chaos, Solitons and Fractals",

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AU - Ivanov, Rossen I.

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N2 - We formulate and study an integrable model of Nonlinear Schrödinger (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.

AB - We formulate and study an integrable model of Nonlinear Schrödinger (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.

KW - Bi-Hamiltonian integrable systems

KW - Derivative nonlinear Schrödinger equation

KW - Hermitian symmetric spaces

KW - Nonlocal integrable equations

KW - Simple Lie algebra

UR - https://www.scopus.com/pages/publications/85132345338

U2 - 10.1016/j.chaos.2022.112299

DO - 10.1016/j.chaos.2022.112299

M3 - Article

AN - SCOPUS:85132345338

SN - 0960-0779

VL - 161

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

M1 - 112299

ER -

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

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Keywords

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