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  • 1. Constantin, A.
    et al.
    Lenells, Jonatan
    Department of Mathematics, Lund University, Lund, Sweden .
    On the inverse scattering approach to the Camassa-Holm equation2003In: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 10, no 3, p. 252-255Article in journal (Refereed)
    Abstract [en]

    A simple algoritm for the inverse scattering approach to the Camassa-Holm equation is presented.

  • 2.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Gauge theory approach towards an explicit solution of the (classical) elliptic Calogero-Moser system2005In: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 12, p. 423-439Article in journal (Refereed)
    Abstract [en]

    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.

  • 3. Larsson, Daniel
    et al.
    Sigurdsson, Gunnar
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Silvestrov, Sergei D.
    On some almost quadratic algebras coming from twisted derivations2006In: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 13, p. 76-86Article in journal (Refereed)
    Abstract [en]

    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.

  • 4. Lenells, J.
    The scattering approach for the Camassa-Holm equation2002In: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 9, no 4, p. 389-393Article in journal (Refereed)
    Abstract [en]

    We present an approach proving the integrability of the Camassa-Holm equation for initial data of small amplitude.

  • 5.
    Lenells, Jonatan
    Lund University, Sweden .
    A variational approach to the stability of periodic peakons2004In: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 11, no 2, p. 151-163Article in journal (Refereed)
    Abstract [en]

    The peakons are peaked traveling wave solutions of an integrable shallow water equation. We present a variational proof of their stability.

  • 6.
    Lenells, Jonatan
    Lund University, Sweden .
    Traveling wave solutions of the Camassa-Holm and Korteweg-de Vries equations2004In: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 11, no 4, p. 508-520Article in journal (Refereed)
    Abstract [en]

    We show that the smooth traveling waves of the Camassa-Holm equation naturally correspond to traveling waves of the Korteweg-de Vries equation.

  • 7.
    Sigurdsson, Gunnar
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Silvestrov, Sergei D.
    Bosonic realizations of the colour Heisenberg Lie algebra2006In: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 13, p. 110-128Article in journal (Refereed)
    Abstract [en]

    We describe realizations of the colour analogue of the Heisenberg Lie algebra by power series in non-commuting indeterminates satisfying Heisenberg's canonical commutation relations of quantum mechanics. The obtained formulas are used to construct new operator representations of the colour Heisenberg Lie algebra. These representations are shown to be closely connected with some combinatorial identities and functional difference-differential interpolation formulae involving Euler numbers.

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