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Lax pair

In mathematics, in the theory of integrable systems, a Lax pair is a pair of time-dependent matrices or operators that satisfy a corresponding differential equation, called the Lax equation. Lax pairs were introduced by Peter Lax to discuss solitons in continuous media. The inverse scattering transform makes use of the Lax equations to solve such systems.

Examples, Isospectral property & Zero-curvature representation

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Definition

Isospectral property

Zero-curvature representation

Examples

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Lax pair

Nodes55
Edges54
Triples44
Avg. degree1.96
Density0.036364
Components1

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Lax pair

Top relations

related to Further examples · 13
Lax pair → Benjamin, Euler, Further, Gordon, Korteweg, Kovalevskaya, Lax, Ono, Petviashvili, Schrödinger, Stewartson, Vries, Zakharov
related to Zero-curvature representation · 11
Lax pair → Any PDE, ASDYM, Furthermore, Gordon, In, Lax, Lax-pair, Mills, PDEs, Ward's, Yang
related to Heisenberg picture · 7
Lax pair → Aside, Hamiltonian, Heisenberg, In, Lax, Planck, The Schrödinger
related to Lax pair to zero-curvature · 6
Lax pair → For, If, Lax, PDE, The Lax, When
related to Definition · 5
Lax pair → Hilbert, Lax, Lax's, Often, PL-LP
is a · 2
Lax pair → pair of matrices or operators L, pair of time-dependent matrices or operators that satisfy a corresponding differential equation

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Important terminology

lax displaystyle equation pair time scattering systems zero-curvature isospectral matrices equations curve representation integrable method picture inverse operators often known

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Lax pairis apair of time-dependent matrices or operators that satisfy a corresponding differential equation0.90text
Lax pairis apair of matrices or operators L0.90text
Lax pairrelated to DefinitionLax0.60section
Lax pairrelated to DefinitionHilbert0.60section
Lax pairrelated to DefinitionLax's0.60section
Lax pairrelated to DefinitionPL-LP0.60section
Lax pairrelated to DefinitionOften0.60section
Lax pairrelated to Further examplesFurther0.60section
Lax pairrelated to Further examplesLax0.60section
Lax pairrelated to Further examplesBenjamin0.60section
Lax pairrelated to Further examplesOno0.60section
Lax pairrelated to Further examplesSchrödinger0.60section

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