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- ...ions''' are an important ingredient in the modern mathematical theory of [[integrable system]]s, and have numerous applications in a variety of other domains. Th ...tor-last1= Harnad | title=Random Matrices, Random Processes and Integrable Systems | series= CRM Series in Mathematical Physics | year=2011 | publisher=Sprin ...43 KB (6,393 words) - 21:02, 25 December 2024
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- {{short description|Result in theory of Hamiltonian systems}} ...n 1971.<ref>{{cite journal| title=Behavior of Hamiltonian systems close to integrable | journal=Functional Analysis and Its Applications | year=1971 | first=Niko ...2 KB (327 words) - 14:21, 29 December 2023
- ...'''modified Korteweg–de Vries (KdV) equation''' is an [[Integrable system|integrable]] nonlinear [[partial differential equation]]:{{sfn | Polyanin | Zaitsev | [[Category:Integrable systems]] ...1 KB (142 words) - 04:02, 3 July 2024
- ...al differential equation]]s that are regarded as being [[Integrable_system|integrable]] or solvable may be obtained from the [[Duality (mathematics)|self-dual]] ...kravarty|last3=Halburd|year=2003|txt}} explain how a variety of completely integrable equations such as the [[Korteweg–De Vries equation]] (KdV) equation, the [[ ...3 KB (355 words) - 12:03, 26 January 2024
- The '''Drinfeld–Sokolov–Wilson (DSW) equations''' are an [[integrable system]] of two coupled [[nonlinear]] [[partial differential equation]]s pr [[Category:Integrable systems]] ...833 bytes (101 words) - 05:57, 13 June 2024
- ...the Liouville-Arnold theorem on [[action-angle coordinates]] of completely integrable Hamiltonian system as follows. ...[[Liouville-Arnold theorem]] for [[Integrable system|completely integrable systems]] and the Mishchenko-Fomenko theorem for the superintegrable ones are gener ...4 KB (490 words) - 12:51, 22 July 2024
- The DBAR problem is of key importance in the theory of [[integrable systems]], [[Schrödinger equation|Schrödinger operators]] and generalizes the [[Rie *{{cite arXiv|last=Konopelchenko |first=B. G.|title=On dbar-problem and integrable equations|year=2000 |eprint=nlin/0002049}} ...2 KB (295 words) - 23:33, 26 August 2024
- The '''Gardner equation''' is an [[integrable]] [[nonlinear partial differential equation]] introduced by the mathematici [[Category:Integrable systems]] ...1 KB (142 words) - 15:09, 16 January 2025
- ...bras]] and have many applications in other areas of algebra and integrable systems. ==Use in integrable systems and relation to the calculus of variations== ...3 KB (449 words) - 19:11, 22 July 2022
- In [[dynamical systems]] theory, the '''Liouville–Arnold theorem''' states that if, in a [[Hamilto ...T. Jones|editor2=Alexander I. Khibnik|title=Multiple-Time-Scale Dynamical Systems|url=https://books.google.com/books?id=LYLkBwAAQBAJ&pg=PA1|year=2012|publish ...7 KB (1,070 words) - 10:00, 3 September 2024
- ...nst equation,'' MathWorld--A Wolfram Web.]</ref> is an [[Integrable system|integrable]] [[non-linear partial differential equation]], named after the American [[ [[Category:Integrable systems]] ...2 KB (290 words) - 20:29, 26 November 2024
- In [[mathematics]], the '''AKNS system''' is an [[integrable system]] of [[partial differential equations]], introduced by and named aft ...rints/pdf/2004/2004024.pdf Huygens’ Principle for Hyperbolic Operators and Integrable Hierarchies]" ...3 KB (341 words) - 20:30, 30 December 2024
- The theory has been used to study [[integrable system]]s through [[four-dimensional Chern–Simons theory]], which can be vi ...cal{W}</math> is fixed to be <math>\mathbb{P}^3</math>. For application to integrable theory, the three form <math>\Omega</math> must be chosen to be [[meromorph ...4 KB (497 words) - 13:17, 4 January 2025
- {{Short description|Method used to solve integrable many-body quantum systems}} ...'''algebraic Bethe ansatz''', is a method for solving [[integrable system|integrable model]]s in 1+1 dimensions, introduced by [[Leon Takhtajan]] and [[Ludvig F ...6 KB (819 words) - 20:40, 9 November 2024
- ...quation |Kadomtsev–Petviashvili]]) integrable hierarchy, and other related integrable hierarchies ...983).</ref> and development of the theory of [[isomonodromic deformation]] systems for rational covariant derivative operators.<ref name="JMU"> M. Jimbo, T. ...3 KB (380 words) - 21:58, 4 May 2024
- ...a discrete version of the [[KdV equation]]. The Volterra lattice is an [[integrable system]], and is related to the [[Toda lattice]]. It is also used as a mode ...fluence of an exponential potential–an integrable system. |title=Dynamical systems, theory and applications (Rencontres, Battelle Res. Inst., Seattle, Wash., ...3 KB (436 words) - 17:22, 14 October 2024
- {{short description|Gauge theory providing unifying formalism for integrable systems}} ...etric space coset [[sigma model]]s and [[Toda field theory]], although the integrable field theories require the introduction of two-dimensional surface defects. ...11 KB (1,586 words) - 13:17, 4 January 2025
- {{Short description|Type of integrable system}} ...crossroads of [[algebraic geometry]], the theory of [[Lie algebra]]s and [[integrable system]] theory. It also plays an important role in the [[geometric Langlan ...8 KB (1,185 words) - 00:43, 20 October 2024
- The '''Gibbons–Tsarev equation''' is an [[Integrable system|integrable]] second order nonlinear [[partial differential equation]].<ref>Andrei D. ...ises in the theory of [[dispersionless equations|dispersionless integrable systems]], as the condition that solutions of the [[Benney moment equations]] may b ...4 KB (591 words) - 23:14, 26 February 2021
- {{Short description|Integrable classical system}} In [[mathematical physics]], the '''Garnier integrable system''', also known as the '''classical Gaudin model''' is a [[classical ...9 KB (1,403 words) - 12:30, 9 July 2023
- ...ble]] random variable (or function). It's also an existence theorem for an integrable random variable (or function). There exist a probabilistic and an analytica *Kabanov, Yuri & Pergamenshchikov, Sergei. (2003). Two-scale stochastic systems. Asymptotic analysis and control. 10.1007/978-3-662-13242-5. Page 250. ...3 KB (404 words) - 11:09, 19 April 2024