Quasi-integrable non-linear Schrödinger models, infinite towers of exactly conserved charges and bright solitons

DOI10.1007/JHEP05(2017)106zbMath1380.81150arXiv1610.07503OpenAlexW2964317910MaRDI QIDQ683002

Juan-Miguel Gracia

Publication date: 5 February 2018

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

Full work available at URL: https://arxiv.org/abs/1610.07503

zbMATH Keywords

integrable hierarchiesintegrable field theoriesspace-time symmetriessolitons monopoles and instantonsnon-linear Schrödinger model (NLS)

Mathematics Subject Classification ID

Soliton equations (35Q51) Groups and algebras in quantum theory and relations with integrable systems (81R12) Geometry and quantization, symplectic methods (81S10) Gravitational energy and conservation laws; groups of motions (83C40)

Related Items (8)

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 ⋮ Majorana zero mode-soliton duality and in-gap and BIC bound states in modified Toda model coupled to fermion ⋮ Quasi-integrability in deformed sine-Gordon models and infinite towers of conserved charges ⋮ Riccati-type pseudo-potentials, conservation laws and solitons of deformed sine-Gordon models ⋮ Analysis and comparative study of non-holonomic and quasi-integrable deformations of the nonlinear Schrödinger equation

Cites Work

• The concept of quasi-integrability: a concrete example
• Two soliton collision for nonlinear Schrödinger equations in dimension 1
• Description of two soliton collision for the quartic gKdV equation
• Numerical methods for the nonlinear Schrödinger equation with nonzero far-field conditions
• Inelastic interactions of solitons in nearly integrable systems. I
• Inelastic interactions of solitons in nearly integrable systems. II
• 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
• Quasi-integrable deformations of the Bullough-Dodd model
• The concept of quasi-integrability for modified nonlinear Schrödinger models
• Quasi-integrability in deformed sine-Gordon models and infinite towers of conserved charges
• Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrödinger equation
• Inelastic interaction of nearly equal solitons for the quartic gKdV equation
• Breather-like structures in modified sine-Gordon models
• A Green’s function for a linear equation associated with solitons
• Perturbations of dark solitons
• Spatial shifts of colliding dark solitons in deformed non-linear Schrödinger models

This page was built for publication: Quasi-integrable non-linear Schrödinger models, infinite towers of exactly conserved charges and bright solitons