| 1. |
- Bouarroudj, Sofian, et al.
(författare)
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DEFINING RELATIONS OF ALMOST AFFINE (HYPERBOLIC) LIE SUPERALGEBRAS
- 2010
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Ingår i: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 17, s. 163-168
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Tidskriftsartikel (refereegranskat)abstract
- For all almost affine (hyperbolic) Lie superalgebras, the defining relations are computed in terms of their Chevalley generators.
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| 2. |
- Carillo, Sandra, et al.
(författare)
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On the recursion operator for the noncommutative Burgers hierarchy
- 2012
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Ingår i: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 19:1, s. Art. no. 1250003-
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Tidskriftsartikel (refereegranskat)abstract
- The noncommutative Burgers recursion operator is constructed via the ColeHopf transformation, and its structural properties are studied. In particular, a direct proof of its hereditary property is given. © S. Carillo and C. Schiebold.
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| 3. |
- Chapovalov, Danil, et al.
(författare)
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THE CLASSIFICATION OF ALMOST AFFINE (HYPERBOLIC) LIE SUPERALGEBRAS
- 2010
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Ingår i: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 17, s. 103-161
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Tidskriftsartikel (refereegranskat)abstract
- We say that an indecomposable Cartan matrix A with entries in the ground field is almost affine if the Lie (super) algebra determined by it is not finite dimensional or affine (Kac-Moody) but the Lie sub(super) algebra determined by any submatrix of A, obtained by striking out any row and any column intersecting on the main diagonal, is the sum of finite dimensional or affine Lie (super) algebras. A Lie (super) algebra with Cartan matrix is said to be almost affine if it is not finite dimensional or affine (Kac-Moody), and all of its Cartan matrices are almost affine. We list all almost affine Lie superalgebras over complex numbers with indecomposable Cartan matrix correcting two earlier claims of classification.
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| 4. |
- Chapovalov, Maxim, et al.
(författare)
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THE POINCARE SERIES OF THE HYPERBOLIC COXETER GROUPS WITH FINITE VOLUME OF FUNDAMENTAL DOMAINS
- 2010
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Ingår i: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 17, s. 169-215
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Tidskriftsartikel (refereegranskat)abstract
- The discrete group generated by reflections of the sphere, or the Euclidean space, or hyperbolic space are said to be Coxeter groups of, respectively, spherical, or Euclidean, or hyperbolic type. The hyperbolic Coxeter groups are said to be (quasi-) Lanner if the tiles covering the space are of finite volume and all (resp. some of them) are compact. For any Coxeter group stratified by the length of its elements, the Poincare series is the generating function of the cardinalities of sets of elements of equal length. Around 1966, Solomon established that, for ANY Coxeter group, its Poincare series is a rational function with zeros somewhere on the unit circle centered at the origin, and gave an implicit (recurrence) formula. For the spherical and Euclidean Coxeter groups, the explicit expression of the Poincare series is well-known. The explicit answer was known for any 3-generated Coxeter group, and (with mistakes) for the Lanner groups. Here we give a lucid description of the numerator of the Poincare series of any Coxeter group, the explicit expression of the Poincare series for each Lanner and quasi-Lanner group, and review the scene. We give an interpretation of some coefficients of the denominator of the growth function. The non-real poles behave as in Enestrom's theorem (lie in a narrow annulus) though the coefficients of the denominators do not satisfy theorem's requirements.
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| 5. |
- Cohen, David, et al.
(författare)
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A multi-symplectic numerical integrator for the two-component Camassa Holm equation
- 2014
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Taylor & Francis. - 1402-9251 .- 1776-0852. ; 21:3, s. 442-453
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Tidskriftsartikel (refereegranskat)abstract
- A new multi-symplectic formulation of the two-component Camassa-Holm equation (2CH) is presented, and the associated local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. A multi-symplectic discretisation based on this new formulation is exemplified by means of the Euler box scheme. Furthermore, this scheme preserves exactly two discrete versions of the Casimir functions of 2CH. Numerical experiments show that the proposed numerical scheme has good conservation properties.
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| 6. |
- Euler, Marianna, et al.
(författare)
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A class of semilinear fifth-order evolution equations : recursion operators and multipotentialisations
- 2011
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Ingår i: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 18:Suppl. 1, s. 61-75
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Tidskriftsartikel (refereegranskat)abstract
- We apply a list of criteria which leads to a class of fifth-order symmetry-integrable evolution equations. The recursion operators for this class are given explicitly. Multipotentialisations are then applied to the equations in this class in order to extend this class of integrable equations.
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| 7. |
- Euler, Marianna, et al.
(författare)
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Invariance of the Kaup-Kupershmidt equation and triangular auto-Bäcklund transformations
- 2012
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Ingår i: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 19:3, s. 1220001/1-1220001/7
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Tidskriftsartikel (refereegranskat)abstract
- We report triangular auto-Bäcklund transformations for the solutions of a fifth-order evolution equation, which is a constraint for an invariance condition of the Kaup-Kupershmidt equation derived by E. G. Reyes in his paper titled ``Nonlocal symmetries and the Kaup-Kupershmidt equation'' [ Math. Phys., 46, 073507, 19 pp., 2005]. These auto-Bäcklund transformations can then be applied to generate solutions of the Kaup-Kupershmidt equation. We show that triangular auto-Bäcklund transformations result from a systematic multipotentialisation of the Kupershmidt equation.
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| 8. |
- Euler, Marianna, et al.
(författare)
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The Two-Component Camassa–Holm Equations CH(2,1) and CH(2,2): First-Order Integrating Factors and Conservation Laws
- 2012
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Ingår i: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 19:Supplement 1, s. 13-22
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Tidskriftsartikel (refereegranskat)abstract
- Recently, Holm and Ivanov, proposed and studied a class of multi-component generalisations of the Camassa-Holm equations [D D Holm and R I Ivanov, Multi-component generalizations of the CH equation: geometrical aspects, peakons and numerical examples, [J. Phys A: Math. Theor, vol. 43, 492001 (20pp), 2010]. We consider two of those systems, denoted by Holm and Ivanov by CH(2,1) and CH(2,2), and report a class of integrating factors and its corresponding conservation laws for these two systems. In particular, we obtain the complete sent of first-order integrating factors for the systems in Cauchy-Kovalevskaya form and evaluate the corresponding sets of conservation laws for CH(2,1) and CH(2,2).
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| 9. |
- Euler, Norbert, et al.
(författare)
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The converse problem for the multipotentialisation of evolution equations and systems
- 2011
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Ingår i: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 18:Suppl. 1, s. 77-105
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Tidskriftsartikel (refereegranskat)abstract
- We propose a method to identify and classify evolution equations and systems that can be multipotentialised in given target equations or target systems. We refer to this as the converse problem. Although we mainly study a method for (1 + 1)-dimensional equations/system, we do also propose an extension of the methodology to higher-dimensional evolution equations. An important point is that the proposed converse method allows one to identify certain types of auto-Bäcklund transformations for the equations/systems. In this respect we define the triangular-auto-Bäcklund transformation and derive its connections to the converse problem. Several explicit examples are given. In particular, we investigate a class of linearisable third-order evolution equations, a fifth-order symmetry-integrable evolution equation as well as linearisable systems.
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| 10. |
- Ibragimov, Nail H.
(författare)
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Lie Group Analysis of Moffatt´s model in Metallurgical Industry
- 2011
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Ingår i: Journal of Nonlinear Mathematical Physics. - : World Scientific Publisher and Atlantis Press. - 1402-9251 .- 1776-0852. ; 18:Suppl. 1
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Tidskriftsartikel (refereegranskat)abstract
- The paper is devoted to the Lie group analysis of a nonlinear equation arising in metallurgical applications of Magnetohydrodynamics. Self-adjointness of the basic equations is investigated. The analysis reveals two exceptional values of the exponent playing a significant role in the model.
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