| 11. |
- Hellström, Lars
(författare)
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Rewriting in operads and PROPs
- 2006
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Ingår i: Journal of nonlinear mathematical physics. - Luleå : Norbert Euler. - 1776-0852 .- 1402-9251. ; , s. 66-75
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Konferensbidrag (refereegranskat)abstract
- This paper is an informal collection of observations on how established rewriting techniques can be applied to or need to be adapted for use in non-associative algebras, operads, and PROPs.
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| 12. |
- Langmann, Edwin
(författare)
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Gauge theory approach towards an explicit solution of the (classical) elliptic Calogero-Moser system
- 2005
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 12, s. 423-439
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Tidskriftsartikel (refereegranskat)abstract
- We discuss the relation of the trigonometric Calogero-Moser (CM) system to Yang-Mills gauge theories and its generalization to the elliptic case. This yields a linearization of the time evolution of the elliptic CM system and suggests two promising strategies for finding a fully explicit solution of this model. We also present a large class of integrable spin-particle systems generalizing the elliptic CM system.
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| 13. |
- Larsson, Daniel, et al.
(författare)
-
On some almost quadratic algebras coming from twisted derivations
- 2006
-
Ingår i: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 13, s. 76-86
-
Tidskriftsartikel (refereegranskat)abstract
- This paper explores the quasi-deformation scheme devised in [1, 3] as applied to the simple Lie algebra sl(2)(F) for specific choices of the involved parameters and underlying algebras. One of the main points of this method is that the quasi-deformed algebra comes endowed with a canonical twisted Jacobi identity. We show in the present article that when the quasi-deformation method is applied to sl(2)(F) one obtains multiparameter families of almost quadratic algebras, and by choosing parameters suitably, sl(2)(F) is quasi-deformed into three-dimensional and four-dimensional Lie algebras and algebras closely resembling Lie superalgebras and colour Lie algebras, this being in stark contrast to the classical deformation schemes where sl(2)(F) is rigid.
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| 14. |
- Larsson, Daniel, et al.
(författare)
-
On some almost quadratic algebras coming from twisted derivations
- 2006
-
Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 13, s. 76-86
-
Tidskriftsartikel (refereegranskat)abstract
- This paper explores the quasi-deformation scheme devised in [1, 3] as applied to the simple Lie algebra sl(2)(F) for specific choices of the involved parameters and underlying algebras. One of the main points of this method is that the quasi-deformed algebra comes endowed with a canonical twisted Jacobi identity. We show in the present article that when the quasi-deformation method is applied to sl(2)(F) one obtains multiparameter families of almost quadratic algebras, and by choosing parameters suitably, sl(2)(F) is quasi-deformed into three-dimensional and four-dimensional Lie algebras and algebras closely resembling Lie superalgebras and colour Lie algebras, this being in stark contrast to the classical deformation schemes where sl(2)(F) is rigid.
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| 15. |
- Leach, Peter, et al.
(författare)
-
A novel Riccati sequence
- 2009
-
Ingår i: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 16:Suppl. 1, s. 157-164
-
Tidskriftsartikel (refereegranskat)abstract
- Hierarchies of evolution partial differential equations have become well-established in the literature over the last thirty years. More recently sequences of ordinary differential equations have been introduced. Of these perhaps the most notable is the Riccati Sequence which has beautiful singularity, symmetry and integrability properties. We examine a variation of this sequence and find that there are some remarkable changes in properties consequential upon this variation.
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| 16. |
- Lundmark, Hans, et al.
(författare)
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Continuous and Discontinuous Piecewise Linear Solutions of the Linearly Forced Inviscid Burgers Equation
- 2008
-
Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 15, s. 264-276
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Tidskriftsartikel (refereegranskat)abstract
- We study a class of piecewise linear solutions to the inviscid Burgers equation driven by a linear forcing term. Inspired by the analogy with peakons, we think of these solutions as being made up of solitons situated at the breakpoints. We derive and solve ODEs governing the soliton dynamics, first for continuous solutions, and then for more general shock wave solutions with discontinuities. We show that triple collisions of solitons cannot take place for continuous solutions, but give an example of a triple collision in the presence of a shock.
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| 17. |
- Mustafa, Octavian
(författare)
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A note on the Degasperis-Procesi equation
- 2005
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 12:1, s. 10-14
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Tidskriftsartikel (refereegranskat)abstract
- We prove that smooth solutions of the Degasperis-Procesi equation have infinite propagation speed: they loose instantly the property of having compact support.
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| 18. |
- Pucacco, Giuseppe, et al.
(författare)
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NONSTANDARD SEPARABILITY ON THE MINKOWSKI PLANE
- 2009
-
Ingår i: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 16:4, s. 421-430
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Tidskriftsartikel (refereegranskat)abstract
- We present examples of nonstandard separation of the natural Hamilton-Jacobi equation on the Minkowski plane M(2). By "nonstandard" we refer to the cases in which the form of the metric, when expressed in separating coordinates, does not have the usual Liouville structure. There are two possibilities: the "complex-Liouville" (or "harmonic") case and the "linear/null" (or "Jordan block") case. By means of explicit examples, we show that, in all cases, a suitable glueing of coordinate patches of the different structures allows us to separate natural systems with indefinite kinetic energy all over M(2).
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| 19. |
- Rauch, Stefan, 1950-, et al.
(författare)
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Triangular newton equations with maximal number of integrals of motion
- 2005
-
Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 12:2, s. 253-267
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Tidskriftsartikel (refereegranskat)abstract
- We study two-dimensional triangular systems of Newton equations (acceleration = velocity-independent force) admitting three functionally independent quadratic integrals of motion. The main idea is to exploit the fact that the first component M1(q1) of a triangular force depends on one variable only. By using the existence of extra integrals of motion we reduce the problem to solving a simultaneous system of three linear ordinary differential equations with nonconstant coefficients for M 1(q1). With the help of computer algebra we have found and solved these ordinary differential equations in all cases. A complete list of superintegrable triangular equations in two dimensions is been given. Most of these equations were not known before.
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| 20. |
- Rauch, Stefan, 1950-, et al.
(författare)
-
What an effective criterion of separability says about the Calogero type systems
- 2005
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 12:SUPPL. 1, s. 535-547
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Tidskriftsartikel (refereegranskat)abstract
- In [15] we have proved a 1-1 correspondence between all separable coordinates on Rn (according to Kalnins and Miller [9]) and systems of linear PDEs for separable potetials V (q). These PDEs, after introducing parameters reflecting the freedom of choice of Euclidean reference frame, serve as an effective criterion of separability. This means that any V (q) satisfying these PDEs is separable and that the separation coordinates can be determined explicitly. We apply this criterion to Calogero systems of particles interacting with each other along a line.
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