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Integrable system

In mathematics, integrability is a property of certain dynamical systems, that means very roughly that the solutions of the system are "simple" enough that they can be written down exactly (in principle). More precisely, while there are several distinct formal definitions, an integrable system can be thought of as a dynamical system with sufficiently…

Some key contributors (since 1965), Integrable systems in 1 + 1 dimensions & Hirota bilinear equations and τ-functions

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Overview

General dynamical systems

Hamiltonian systems and Liouville integrability

Action-angle variables

The Hamilton–Jacobi approach

Solitons and inverse spectral methods

Hirota bilinear equations and τ-functions

Algebraic integrability

Diophantine integrability

Quantum integrable systems

Classical mechanical systems

Integrable lattice models

Integrable systems in 1 + 1 dimensions

Integrable PDEs in 2 + 1 dimensions

Integrable PDEs in 3 + 1 dimensions

Exactly solvable statistical lattice models

Discrete integrable systems

Some key contributors (since 1965)

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Integrable system

Nodes162
Edges161
Triples187
Avg. degree1.99
Density0.012346
Components1

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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

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Important terminology

systems integrable hamiltonian integrability system isbn dynamical sense foliation complete space set quantum liouville solutions equations completely leaves variables invariant

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SubjectPredicateObjectConfidenceSrc
latticesinstance ofwhich is what is most frequently referred to in this context.An extension of the notion of integrability is also applicable to discrete systems0.80text
solitons could be derived.Subsequentlyinstance ofthis nevertheless gave a very direct method from which important classes of solutions0.80text
this was interpreted by Mikio Satoinstance ofthis nevertheless gave a very direct method from which important classes of solutions0.80text
his studentsinstance ofthis nevertheless gave a very direct method from which important classes of solutions0.80text
at first for the case of integrable hierarchies of PDEsinstance ofthis nevertheless gave a very direct method from which important classes of solutions0.80text
such as the Kadomtsevinstance ofthis nevertheless gave a very direct method from which important classes of solutions0.80text
Integrable systemhas methodKorteweg0.60section
Integrable systemhas methodVries0.60section
Integrable systemhas methodHamiltonian0.60section
Integrable systemhas methodTheir0.60section
Integrable systemhas methodRiemann0.60section
Integrable systemhas methodHilbert0.60section

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