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  • 1. Berntson, Bjorn K. K.
    et al.
    Langmann, Edwin
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Lenells, Jonatan
    Elliptic soliton solutions of the spin non-chiral intermediate long-wave equation2023In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 113, no 3, article id 61Article in journal (Refereed)
    Abstract [en]

    We construct elliptic multi-soliton solutions of the spin non-chiral intermediate long-wave (sncILW) equation with periodic boundary conditions. These solutions are obtained by a spin-pole ansatz including a dynamical background term; we show that this ansatz solves the periodic sncILW equation provided the spins and poles satisfy the elliptic A-type spin Calogero-Moser (sCM) system with certain constraints on the initial conditions. The key to this result is a Backlund transformation for the elliptic sCM system which includes a non-trivial dynamical background term. We also present solutions of the sncILW equation on the real line and of the spin Benjamin-Ono equation which generalize previously obtained solutions by allowing for a non-trivial background term.

  • 2. Berntson, Bjorn K.
    et al.
    Langmann, Edwin
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). KTH Royal Institute of Technology, Sweden.
    Lenells, J.
    Spin generalizations of the Benjamin–Ono equation2022In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 112, no 3, article id 50Article in journal (Refereed)
    Abstract [en]

    We present new soliton equations related to the A-type spin Calogero–Moser (CM) systems introduced by Gibbons and Hermsen. These equations are spin generalizations of the Benjamin–Ono (BO) equation and the recently introduced non-chiral intermediate long-wave (ncILW) equation. We obtain multi-soliton solutions of these spin generalizations of the BO equation and the ncILW equation via a spin-pole ansatz where the spin-pole dynamics is governed by the spin CM system in the rational and hyperbolic cases, respectively. We also propose physics applications of the new equations, and we introduce a spin generalization of the standard intermediate long-wave equation which interpolates between the matrix Korteweg-de Vries equation, the Heisenberg ferromagnet equation, and the spin BO equation.

  • 3.
    Kurasov, Pavel
    Stockholm University, Faculty of Science, Department of Mathematics.
    On the ground state for quantum graphs2019In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 109, no 11, p. 2491-2512Article in journal (Refereed)
    Abstract [en]

    Ground-state eigenfunctions of Schrodinger operators can often be chosen positive. We analyse to which extent this is true for quantum graphs-differential operators on metric graphs. It is shown that the theorem holds in the case of generalised delta couplings at the vertices-a new class of vertex conditions introduced in the paper. It is shown that this class of vertex conditions is optimal. Relations to positivity preserving and positivity improving semigroups are clarified.

  • 4.
    Kurasov, Pavel
    Stockholm University.
    Zero-range potentials with internal structures and the inverse scattering problem1992In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530Article in journal (Refereed)
  • 5.
    Kurasov, Pavel
    et al.
    Stockholm University.
    Albeverio, io
    Dabrowski, Ludvig
    Symmetries of Schr�dinger operator with point interactions1998In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530Article in journal (Refereed)
  • 6.
    Kurasov, Pavel
    et al.
    Stockholm University.
    Albeverio, Sergio
    Pseudo-differential operators with point interactions1997In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530Article in journal (Refereed)
  • 7.
    Kurasov, Pavel
    et al.
    Stockholm University.
    Albeverio, Sergio
    Fei, Shao-Ming
    Point interactions: PT-Hermiticity and reality of the spectrum2002In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530Article in journal (Refereed)
  • 8.
    Kurasov, Pavel
    et al.
    Stockholm University.
    Luger, Annemarie
    Stockholm University, Faculty of Science, Department of Mathematics.
    Reflectionless Potentials and Point Interactions in Pontryagin Spaces2005In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530Article in journal (Refereed)
  • 9.
    Kurasov, Pavel
    et al.
    Stockholm University.
    Pavlov, Yuri
    On field theory methods in singular perturbation theory2003In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530Article in journal (Refereed)
  • 10.
    Merkulov, Sergei A.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Formality Theorem for Quantizations of Lie Bialgebras2016In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 106, no 2, p. 169-195Article in journal (Refereed)
    Abstract [en]

    Using the theory of props we prove a formality theorem associated with universal quantizations of Lie bialgebras.

  • 11.
    Merkulov, Sergei
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Willwacher, Thomas
    Grothendieck-Teichmuller and Batalin-Vilkovisky2014In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 104, no 5, p. 625-634Article in journal (Refereed)
    Abstract [en]

    It is proven that, for any affine supermanifold M equipped with a constant odd symplectic structure, there is a universal action (up to homotopy) of the Grothendieck Teichmuller Lie algebra grt(1) on the set of quantum BV structures (i.e. solutions of the quantum master equation) on M.

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