The concept of quasi-integrability for modified nonlinear Schrödinger models

DOI10.1007/JHEP09(2012)103zbMath1397.81095arXiv1206.5808OpenAlexW2080134171MaRDI QIDQ1795989

G. Luchini, Luiz Agostinho Ferreira, Wojciech J. Zakrzewski

Publication date: 16 October 2018

Published in: Journal of High Energy Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.5808

zbMATH Keywords

integrable hierarchiesintegrable field theoriesintegrable equations in physicssolitons monopoles and instantons

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Groups and algebras in quantum theory and relations with integrable systems (81R12) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20)

Related Items (16)

Quasi-integrability in the modified defocusing non-linear Schrödinger model and dark solitons ⋮ Collective coordinate approximation to the scattering of solitons in modified NLS and sine-Gordon models ⋮ Study of quasi-integrable and non-holonomic deformation of equations in the NLS and DNLS hierarchy ⋮ Modified nonlinear Schrödinger models, 𝒞𝒫s𝒯d invariant N-bright solitons and infinite towers of anomalous charges ⋮ Non-holonomic and quasi-integrable deformations of the AB equations ⋮ Quasi-integrable KdV models, towers of infinite number of anomalous charges and soliton collisions ⋮ Quasi-integrability in deformed sine-Gordon models and infinite towers of conserved charges ⋮ Quasi-integrability of deformations of the KdV equation ⋮ Riccati-type pseudo-potentials, conservation laws and solitons of deformed sine-Gordon models ⋮ Resonance structures in kink-antikink collisions in a deformed sine-Gordon model ⋮ Quasi-integrable non-linear Schrödinger models, infinite towers of exactly conserved charges and bright solitons ⋮ Quasi-integrable deformations of the Bullough-Dodd model ⋮ Analysis and comparative study of non-holonomic and quasi-integrable deformations of the nonlinear Schrödinger equation ⋮ Some aspects of self-duality and generalised BPS theories ⋮ Quasi-Integrability and Some Aspects of SU(3) Toda Field Theory ⋮ Soliton-like behaviour in non-integrable systems

Cites Work

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• The concept of quasi-integrability: a concrete example
• Classical behavior of deformed sine-gordon models
• Lie algebras and equations of Korteweg-de Vries type
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• THE CONSERVED CHARGES AND INTEGRABILITY OF THE CONFORMAL AFFINE TODA MODELS
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• Introduction to Classical Integrable Systems
• Integrals of nonlinear equations of evolution and solitary waves

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