Journal of Nonlinear Mathematical Physics

Volume 23, Issue 1, January 2016, Pages 108 - 126

Ermakov-Modulated Nonlinear Schrödinger Models. Integrable Reduction

Authors
Colin Rogers
Australian Research Council Centre of Excellence for Mathematics & Statistics of Complex Systems, School of Mathematics, The University of New South Wales, Sydney, NSW2052, Australia, c.rogers@unsw.edu.au
Giuseppe Saccomandi
Dipartimento di Ingegneria Industriale, Università degli Studi di Perugia, I-06125, Perugia, Italy.
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, University Road, Galway, Ireland. giuseppe.saccomandi@unipg.it
Luigi Vergori
School of Mathematics and Statistics, University of Glasgow, University Gardens 15 G128QW Glasgow, United Kingdom. luigi.vergori@glasgow.ac.uk
Received 1 September 2015, Accepted 1 October 2015, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2016.1135645How to use a DOI?
Keywords
Nonlinear Schödinger models, Ermakov reduction, Nonlinear waves
Abstract

Nonlinear Schrödinger equations with spatial modulation associated with integrable Hamiltonian systems of Ermakov-Ray-Reid type are introduced. An algorithmic procedure is presented which exploits invariants of motion to construct exact wave packet representations with potential applications in a wide range of physical contexts such as, ‘inter alia’, the analysis of Bloch wave and matter wave solitonic propagation and pulse transmission in Airy modulated NLS models. A particular Ermakov reduction for Mooney-Rivlin materials is set in the broader context of transverse wave propagation in a class of higher-order hyperelastic models of incompressible solids.

Copyright
© 2016 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
23 - 1
Pages
108 - 126
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2016.1135645How to use a DOI?
Copyright
© 2016 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Colin Rogers
AU  - Giuseppe Saccomandi
AU  - Luigi Vergori
PY  - 2021
DA  - 2021/01
TI  - Ermakov-Modulated Nonlinear Schrödinger Models. Integrable Reduction
JO  - Journal of Nonlinear Mathematical Physics
SP  - 108
EP  - 126
VL  - 23
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2016.1135645
DO  - https://doi.org/10.1080/14029251.2016.1135645
ID  - Rogers2021
ER  -