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Explore the main themes, entities and connections around Integrable system. Start with the topic map, then use the sections below for research and deeper semantic analysis.
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Some key contributors (since 1965)
20 related topics
Integrable systems in 1 + 1 dimensions
AKNS systemBenjamin–Ono equationBoussinesq equation (water waves)Camassa–Holm equationClassical Heisenberg ferromagnet model (spin chain)
14 related topics
Hirota bilinear equations and τ-functions
11 related topics
Quantum integrable systems
11 related topics
Key facts & relationships
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Topics to explore
A structured outline of related entities, concepts and subtopics. Open any item to build a new map centered on it.Browse the full topic structure. Each item opens a new analysis centered on that subject.
Overview
- Dynamical systems Dynamical system
- Conserved quantities Conserved quantity
- First integrals First integral
- Phase space
- Chaotic systems Chaotic system
- Algebraic geometry
- Chaotic systems Chaos theory
- Hamiltonian Hamiltonian system
- Euler top
- Lagrange top
- Korteweg–de Vries equation
- Kerr effect
- Nonlinear Schrödinger equation
- Toda lattice
- Solitons
- Martin Kruskal
- Norman Zabusky
- Inverse scattering transform
- Lagrangian foliation
- Liouville–Arnold theorem
- Action-angle variables
- Frobenius theorem Frobenius theorem (differential topology)
- Foliation
- Dynamical systems
- Special functions
General dynamical systems
- Embedded submanifolds Embedded submanifold
- Flow Flow (mathematics)
- Hamiltonian systems Hamiltonian mechanics
- Liouville
- Differential equations
- Finite difference equations Finite difference
- Chaotic motion
Hamiltonian systems and Liouville integrability
- Hamiltonian systems Hamilton's equations
- Liouville Joseph Liouville
- Poisson brackets Poisson bracket
- Symplectic Symplectic geometry
- Lagrangian Lagrangian submanifold
- Tori Torus
- Superintegrable Superintegrable Hamiltonian system
Action-angle variables
- Canonical coordinates
- Action Action (physics)
The Hamilton–Jacobi approach
- Canonical transformation
- Hamilton–Jacobi Hamilton–Jacobi equations
- Hamilton–Jacobi equation
- Separation of variables
Solitons and inverse spectral methods
- Solitons Soliton
- Riemann–Hilbert problems Riemann–Hilbert problem
- Lax pair
Hirota bilinear equations and τ-functions
- Τ-function Tau function (integrable systems)
- Mikio Sato
- Kadomtsev–Petviashvili Kadomtsev–Petviashvili equation
- Group action
- Grassmann manifold Grassmannian
- Determinant
- Projection operator
- Group orbit
- Plücker relations Plücker embedding
- Exterior space Exterior algebra
- Fermionic Fock space Fock space
Algebraic integrability
- Rational map Birational geometry
- Non-singular Non-singular algebraic variety
- Affine variety
- Hamiltonian Hamiltonian vector field
- Generic Generic point
- Level set
- Abelian variety
- Jacobian Jacobian variety
- Spectral curve
- Translation invariant
Diophantine integrability
- Projective space
- Finite field
- Rational point
- Height Height function
Quantum integrable systems
- Self-adjoint operators
- Hilbert space
- Local Principle of locality
- Hamiltonian Hamiltonian (quantum mechanics)
- Eigenstates
- Yang–Baxter equation
- Quantum inverse scattering method
- Bethe ansatz
- Lieb–Liniger model
- Hubbard model
- Heisenberg model Heisenberg model (quantum)
Classical mechanical systems
Integrable lattice models
Integrable systems in 1 + 1 dimensions
- AKNS system
- Benjamin–Ono equation
- Boussinesq equation (water waves)
- Camassa–Holm equation
- Classical Heisenberg ferromagnet model (spin chain)
- Degasperis–Procesi equation
- Dym equation
- Garnier integrable system
- Kaup–Kupershmidt equation
- Landau–Lifshitz equation (continuous spin field)
- Nonlinear sigma models
- Sine–Gordon equation
- Thirring model
- Three-wave equation
Integrable PDEs in 2 + 1 dimensions
Integrable PDEs in 3 + 1 dimensions
- Belinski–Zakharov transform
- Einstein field equations Einstein field equation
- Gravitational solitons Gravitational soliton
- Schwarzschild metric
- Kerr metric
- Gravitational wave
Exactly solvable statistical lattice models
Discrete integrable systems
- Its generalisations Pentagram map
Some key contributors (since 1965)
- Mark Ablowitz
- Rodney Baxter
- Percy Deift
- Vladimir Drinfeld
- Boris Dubrovin Boris Dubrovin (mathematician)
- Ludvig Faddeev
- Hermann Flaschka
- Israel Gel'fand
- Alexander Its
- Michio Jimbo
- Igor M. Krichever Igor Krichever
- Peter Lax
- Robert Miura
- Tetsuji Miwa
- Alan Newell Alan C. Newell
- Nicolai Reshetikhin
- Evgeny Sklyanin
- Elliott H. Lieb
- Graeme Segal
- Vladimir E. Zakharov
Advanced semantic analysis
Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.
Map overview Semantic statistics
Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.Integrable system
Nodes162
Edges161
Triples187
Avg. degree1.99
Density0.012346
Components1
How this topic connects Entity context
Quick relationship hints grouped by predicate. Useful for spotting recurring semantic connections around the current entity.See the strongest relationship patterns around the current topic before diving into the raw triples.
Integrable system
Top relations
related to References · 86
Integrable system → Academic Press, Addison-Wesley, Advanced Mathematics, Afrajmovich, American Mathematical Society, An Introduction, Applications, Arnold, Audin, Babelon, Balogh, Baxter, Bernard, Bibcode, Bogoliubov, Bolsinov, Breach, Cambridge Monographs, Cambridge Studies, Cambridge University Press
related to Further reading · 28
Integrable system → Beilinson, BFb0094792, Bibcode, Cary, CS1, Donagi, Drinfeld, Finding, Hamiltonian, Hecke, Hitchin's, Integrable, ISBN, John, Kiran, Lecture Notes, Lie, Markman, Mathematics, PDF
related to Hirota bilinear equations and τ-functions · 16
Integrable system → Although, Another, Fock, Grassmann, Grassmannian, Hamiltonian, Hirota, Kadomtsev, Mikio Sato, PDEs, Petviashvili, Plücker, Ryogo Hirota, Subsequently, The, These
has method · 14
Integrable system → Fourier, Hamiltonian, Hilbert, However, In, KdV, Korteweg, Lax, Liouville, Riemann, The, Their, This, Vries
related to Integrable systems in 1 + 1 dimensions · 13
Integrable system → AKNS, Camassa, Degasperis, Gordon, Heisenberg, Holm, Kupershmidt, Lifshitz, Nonlinear Schrödinger, Novikov, Ono, Procesi, Vries
related to Exactly solvable models · 9
Integrable system → Baxter, Bethe, Hamiltonian, In, There, These, This, Two, Yang
related to External links · 8
Integrable system → Difference Equations, EMS Press, Encyclopedia, Integrability, Integrable, Mathematics, SIDE, Symmetries
related to Quantum integrable systems · 7
Integrable system → Every Hamiltonian, Hilbert, However, In, Poisson, The, There
Important terminology Word statistics
Frequent words and multi-word phrases across the lead, headings, infobox and body. Useful for terminology coverage.Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.
Important terminology
systems integrable hamiltonian integrability system isbn dynamical sense foliation complete space set quantum liouville solutions equations completely leaves variables invariant
Entity relationships Subject–Predicate–Object triples
Extracted RDF-like relationships with confidence and source. The table includes structured facts and lower-confidence contextual relations.| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| lattices | instance of | which is what is most frequently referred to in this context.An extension of the notion of integrability is also applicable to discrete systems | 0.80 | text |
| solitons could be derived.Subsequently | instance of | this nevertheless gave a very direct method from which important classes of solutions | 0.80 | text |
| this was interpreted by Mikio Sato | instance of | this nevertheless gave a very direct method from which important classes of solutions | 0.80 | text |
| his students | instance of | this nevertheless gave a very direct method from which important classes of solutions | 0.80 | text |
| at first for the case of integrable hierarchies of PDEs | instance of | this nevertheless gave a very direct method from which important classes of solutions | 0.80 | text |
| such as the Kadomtsev | instance of | this nevertheless gave a very direct method from which important classes of solutions | 0.80 | text |
| Integrable system | has method | Korteweg | 0.60 | section |
| Integrable system | has method | Vries | 0.60 | section |
| Integrable system | has method | Hamiltonian | 0.60 | section |
| Integrable system | has method | Their | 0.60 | section |
| Integrable system | has method | Riemann | 0.60 | section |
| Integrable system | has method | Hilbert | 0.60 | section |
No triples extracted yet.
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Connections between topic areas Semantic bridges
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