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Knotted solutions for linear and nonlinear theories: Electromagnetism and fluid dynamics

https://doi.org/10.1016/j.physletb.2017.08.063

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Compressible helical flows

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Topological Methods in Hydrodynamics

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A topological theory of the electromagnetic field

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Solutions of the Maxwell and Yang-Mills equations associated with hopf fibrings

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The quantum mechanics of perfect fluids

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Optical knots and contact geometry I. From Arnol’d inequality to Ranada’s dyons

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Motion of magnetic lines of force

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On the topological meaning of canonical Clebsch variables

inferredcites →https://doi.org/10.1016/j.aop.2016.04.003openalex-snapshot

Optical knots and contact geometry II. From Ranada dyons to transverse and cosmetic knots

inferredcites →https://doi.org/10.1016/j.jnnms.2014.12.002openalex-snapshot

Vortical structures on spherical surfaces

inferredcites →https://doi.org/10.1016/j.physrep.2016.11.001openalex-snapshot

Knots in electromagnetism

inferredcites →https://doi.org/10.1017/s0022112003007043openalex-snapshot

Stuart vortices on a sphere

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The degree of knottedness of tangled vortex lines

inferredcites →https://doi.org/10.1038/nphys2560openalex-snapshot

Creation and dynamics of knotted vortices

inferredcites →https://doi.org/10.1063/1.869762openalex-snapshot

Analogy between the Navier–Stokes equations and Maxwell’s equations: Application to turbulence

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Topological Ideas and Fluid Mechanics

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Electromagnetic fields with vanishing scalar invariants

inferredcites →https://doi.org/10.1088/0305-4470/23/16/007openalex-snapshot

Knotted solutions of the Maxwell equations in vacuum

inferredcites →https://doi.org/10.1088/0741-3335/52/12/124002openalex-snapshot

Mathematics and Maxwell's equations

inferredcites →https://doi.org/10.1088/1751-8113/43/38/385203openalex-snapshot

Linked and knotted beams of light, conservation of helicity and the flow of null electromagnetic fields

inferredcites →https://doi.org/10.1088/1751-8113/48/2/025203openalex-snapshot

A class of non-null toroidal electromagnetic fields and its relation to the model of electromagnetic knots

inferredcites →https://doi.org/10.1088/1751-8113/48/25/255204openalex-snapshot

New knotted solutions of Maxwell's equations

inferredcites →https://doi.org/10.1098/rspa.1934.0059openalex-snapshot

Foundations of the new field theory

inferredcites →https://doi.org/10.1098/rspa.1992.0159openalex-snapshot

Helicity and the Călugăreanu invariant

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Effective field theory for hydrodynamics: Thermodynamics, and the derivative expansion

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More on Heisenberg’s model for high energy nucleon-nucleon scattering

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DBI scalar field theory for QGP hydrodynamics

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Universe without dark energy: Cosmic acceleration from dark matter-baryon interactions

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Turbulent transport of a tracer: An electromagnetic formulation

inferredcites →https://doi.org/10.1103/physreve.85.036306openalex-snapshot

Vortex knots in a Bose-Einstein condensate

inferredcites →https://doi.org/10.1103/physrevlett.111.150404openalex-snapshot

Tying Knots in Light Fields

inferredcites →https://doi.org/10.1140/epjp/i2013-13081-5openalex-snapshot

Forty years of Galilean Electromagnetism (1973–2013)

inferredcites →https://doi.org/10.1142/9789812775344_0014openalex-snapshot

HEISENBERG–EULER EFFECTIVE LAGRANGIANS: BASICS AND EXTENSIONS

inferredcites →https://doi.org/10.1143/jpsj.31.591openalex-snapshot

Motion of Distorted Vortex Rings

inferredcites →https://doi.org/10.1146/annurev.fl.24.010192.001433openalex-snapshot

Helicity in Laminar and Turbulent Flow

inferredcites →https://doi.org/10.1146/annurev.fluid.24.1.281openalex-snapshot

Helicity In Laminar And Turbulent Flow

inferredcites →https://doi.org/10.1209/0295-5075/115/10004openalex-snapshot

Nonlinear electrodynamics is skilled with knots

inferredcites →https://doi.org/10.1393/ncc/i2009-10355-2openalex-snapshot

New developments in topological fluid mechanics

inferredcites →https://doi.org/10.4064/-42-1-321-346openalex-snapshot

Applications of knot theory in fluid mechanics

inferredcites →https://doi.org/10.48550/arxiv.1106.1122openalex-snapshot

Electromagnetic Torus Knots

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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inferred← citeshttps://doi.org/10.1002/prop.201800042openalex-snapshot

Lagrangian Formulation, Generalizations and Quantization of Null Maxwell's Knots

inferred← citeshttps://doi.org/10.1007/jhep07(2025)015openalex-snapshot

Nonabelian fluids and helicities

inferred← citeshttps://doi.org/10.1007/jhep12(2022)144openalex-snapshot

Fluid-electromagnetic helicities and knotted solutions of the fluid-electromagnetic equations

inferred← citeshttps://doi.org/10.1007/s11227-021-03917-yopenalex-snapshot

Field equations for incompressible non-viscous fluids using artificial intelligence

inferred← citeshttps://doi.org/10.1016/j.aop.2026.170357openalex-snapshot

Non-null torus knotted gravitational waves from gravitoelectromagnetism

inferred← citeshttps://doi.org/10.1016/j.physleta.2023.129285openalex-snapshot

Gauge theories for fluids in 2 + 1 dimensions through master actions

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Monochromatic knots and other unusual electromagnetic disturbances: light localised in 3D

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Boundary Witten effect in multiaxion insulators

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Coupling the precursor of the most general theory of electromagnetism invariant under duality and conformal invariance with scalars, and BIon-type solutions

inferred← citeshttps://doi.org/10.1103/physrevd.107.125011openalex-snapshot

Charged soliton of the three-dimensional CS+BI Abelian gauge theory

inferred← citeshttps://doi.org/10.1103/physrevd.109.085006openalex-snapshot

Euler fluid in 2+1 dimensions as a gauge theory and an action for the Euler fluid in any dimension

inferred← citeshttps://doi.org/10.1103/physrevd.110.125019openalex-snapshot

Novel knotted non-Abelian gauge fields

inferred← citeshttps://doi.org/10.1103/physrevd.97.084041openalex-snapshot

Spacetimes dressed with stealth electromagnetic fields

inferred← citeshttps://doi.org/10.1140/epjc/s10052-020-8123-3openalex-snapshot

Finsler geometries from topological electromagnetism

inferred← citeshttps://doi.org/10.1140/epjc/s10052-023-11856-6openalex-snapshot

The shapes of the knots corresponding to the special Hopfions

inferred← citeshttps://doi.org/10.1142/s0217751x17502001openalex-snapshot

Knotted solutions, from electromagnetism to fluid dynamics

inferred← citeshttps://doi.org/10.1142/s0217751x20501134openalex-snapshot

Nonlinear dynamics of a charged particle in a strong non-null knot wave background

inferred← citeshttps://doi.org/10.1142/s0219887818500548openalex-snapshot

On the existence of the field line solutions of the Einstein–Maxwell equations

inferred← citeshttps://doi.org/10.1364/prj.533264openalex-snapshot

Sculpting isolated optical vortex knots on demand

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Perspective Study of Fluid Dynamics towards Engineering Students: A Short Review

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Deep Learning Driven Enhancement of Optical Vortex Line Robustness in Atmospheric Turbulence

inferred← citeshttps://doi.org/10.3390/universe7030046openalex-snapshot

Gravitoelectromagnetic Knot Fields

inferred← citeshttps://doi.org/10.3390/universe7030065openalex-snapshot

Nonperturbative Quantization Approach for QED on the Hopf Bundle

inferred← citeshttps://doi.org/10.48550/arxiv.1812.08630openalex-snapshot

Hopfion solutions in gravity and a null fluid/gravity conjecture

inferred← citeshttps://doi.org/10.48550/arxiv.1911.04486openalex-snapshot

Knots and the Maxwell Equations

inferred← citeshttps://doi.org/10.48550/arxiv.2105.10062openalex-snapshot

Gravity and its wonders: braneworlds and holography

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Coupling ModMax theory precursor with scalars, and BIon-type solutions

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