Noncommutative Burgers equation

“…The existence of infinite number of conserved quantities would lead to infinite-dimensional hidden symmetry from Noether's theorem. First we would like to comment on conservation laws of NC field equations 68 . The discussion is basically the same as commutative case because both the differentiation and the integration are the same as commutative ones in the Moyal representation.…”

Section: Conservation Lawsmentioning

confidence: 99%

Noncommutative Solitons and Integrable Systems

Hamanaka

2005

Noncommutative Geometry and Physics

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We review recent developments of soliton theories and integrable systems on noncommutative spaces. The former part is a brief review of noncommutative gauge theories focusing on ADHM construction of noncommutative instantons. The latter part is a report on recent results of existence of infinite conserved densities and exact multi-soliton solutions for noncommutative Gelfand-Dickey hierarchies. Some examples of noncommutative Ward's conjecture are also presented. Finally, we discuss future directions on noncommutative Sato's theories and twistor theories.

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“…The methods outlined in this talk have also been applied successfully towards the construction and study of various other noncommutative field configurations (see for example [10,11,12,13] and references therein 2 ). In my group, in particular, we have investigated [14,15,16,17,18] • …”

Section: D=4+0: Instantons In Noncommutative Yang-millsmentioning

confidence: 99%

Noncommutative instantons and solitons

Lechtenfeld

2004

Fortschritte der Physik

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I explain how to construct noncommutative BPS configurations in four and lower dimensions by solving linear matrix equations. Examples are instantons in D=4 Yang-Mills, monopoles in D=3 Yang-Mills-Higgs, and (moving) solitons in D=2+1 YangMills-Higgs. Some emphasis is on the latter as a showcase for the dressing method. Self-duality and BPS equationsIn this talk I shall present a powerful method for and results of constructing classical field configurations with finite action or energy in four-dimensional noncommutative gauge theory and its lower-dimensional descendants:I am setting up the formalism in such a way that it is completely transparent to the (Moyal-type) noncommutative deformation. In other words, the noncommutative equations below differ from the commutative ones merely in the interpretation of the symbols or their product (stars are suppressed). This will be briefly explained in Section 6. The Yang-Mills field equations are implied by first-order (self-duality or BPS) equations:where F and φ are u(n) valued and Greek indices run from 1 to 4 while Latin ones stop at 3. In complex coordinates (note the signs!) y = x 1 +ix 2 and z = x 3 ∓ix 4 the self-duality equationwhere the upper and lower signs belong to the signatures (4,0) and (2,2), respectively. Dimensional reduction to D=3 is accomplished via

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Noncommutative Burgers equation

Cited by 49 publications

References 57 publications

Extensions of Soliton equations to non-commutative (2 + 1) dimensions

Extensions of Soliton equations to non-commutative (2 + 1) dimensions

Noncommutative Solitons and Integrable Systems

Noncommutative instantons and solitons

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