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  • 1. Ibragimov, N. H.
    et al.
    Kolsrud, Torbjörn
    KTH, Tidigare Institutioner, Matematik.
    Lagrangian approach to evolution equations: Symmetries and conservation laws2004Inngår i: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 36, nr 1, s. 29-40Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We show that one can apply a Lagrangian approach to certain evolution equations by considering them together with their associated equations. Consequently, one can employ Noether's theorem and derive conservation laws from symmetries of coupled systems of evolution equations. We discuss in detail the linear and non-linear heat equations as well as the Burgers equation and obtain new non-local conservation laws for the non-linear heat and the Burgers equations by extending their symmetries to the associated equations. We also provide Lagrangians for non-linear Schrodinger and Korteweg-de Vries type systems.

  • 2. Iwata, Koichiro
    et al.
    Kolsrud, Torbjörn
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Central limit theorem for constrained Poisson systems2009Inngår i: Bulletin des Sciences Mathématiques, ISSN 0007-4497, E-ISSN 1952-4773, Vol. 133, nr 6, s. 658-669Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove that for a class of constrained Poisson white noise fields. the scaling (continuum) limit exists and equals Gaussian white noise. indexed by mean zero test functions. Under natural conditions on the Levy measure, the (Poisson) moments converge to their Gaussian counterparts.

  • 3.
    Kolsrud, Torbjörn
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Position dependent non-linear Schrodinger hierarchies: Involutivity, commutation relations, renormalisation and classical invariants2006Inngår i: Bulletin des Sciences Mathématiques, ISSN 0007-4497, E-ISSN 1952-4773, Vol. 130, nr 8, s. 739-756Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider a family of explicitly position dependent hierarchies (I-n)(0)(infinity), containing the NLS (non-linear Schrodinger) hierarchy. All (I-n)(0)(infinity) are involutive and fulfill DIn = nI(n-1), where D = D-1 V-0, V-0 being the Hamiltonian vector field v delta/delta v - u delta/delta u afforded by the common ground state I-0 = uv. The construction requires renormalisation of certain function parameters. It is shown that the 'quantum space' C[I-0, I-1,...] projects down to its classical counterpart C[p], with p = I-1/I-0, the momentum density. The quotient is the kernel of D. It is identified with classical semi-invariants for forms in two variables.

  • 4.
    Kolsrud, Torbjörn
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Quantum and classical conserved quantities: Martingales, conservation laws and constants of motion2007Inngår i: Stochastic Analysis and Applications / [ed] Benth, FE; DiNunno, G; Lindstrom, T; Oksendal, B; Zhang, T, 2007, Vol. 2, s. 461-491Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We study a class of diffusions, conjugate Brownian motion, related to Brownian motion in Riemannian manifolds. Mappings that, up to a change of time scale, carry these processes into each other, are characterised. The characterisation involves conformality and a space-time version of harmonicity. Infinitesimal descriptions are given and used to produce martingales and conservation laws. The relation to classical constants of motion is presented, as well as the relation to Noether's theorem in classical mechanics and field theory.

  • 5.
    Kolsrud, Torbjörn
    et al.
    KTH, Tidigare Institutioner                               , Matematik.
    Loubeau, E.
    Foliated manifolds and conformal heat morphisms2002Inngår i: Annals of Global Analysis and Geometry, ISSN 0232-704X, E-ISSN 1572-9060, Vol. 21, nr 3, s. 241-267Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The objects under study, in this article, are Riemannian manifolds foliated by hypersurfaces. Looking at the transverse direction as time, we construct the generalised heat operator and, in the spirit of a time-space extension of harmonic morphisms, we introduce the conformal heat morphisms. Concrete examples of these concepts are presented, as well as, a characterisation of conformal heat morphisms. Lastly, we calculate the heat Lie algebra of the generalised heat operator.

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