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Structure of Noncommutative Solitons: Existence and Spectral Theory

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Abstract

We consider the Schrödinger equation with a Hamiltonian given by a second-order difference operator with nonconstant growing coefficients, on the half one-dimensional lattice. This operator appeared first naturally in the construction and dynamics of noncommutative solitons in the context of noncommutative field theory. We construct a ground state soliton for this equation and analyze its properties. In particular, we arrive at \({\ell^{\infty}}\) and \({\ell^{1}}\) estimates as well as a quasi-exponential spatial decay rate.

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Authors and Affiliations

  1. Technion Mathematics Department, Amado Building, 32000, Haifa, Israel

    August J. Krueger

  2. Rutgers Mathematics Department, 110 Frelinghuysen Rd., Piscataway, NJ, 08854, USA

    Avy Soffer

Authors
  1. August J. Krueger
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  2. Avy Soffer
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Correspondence to August J. Krueger.

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Krueger, A.J., Soffer, A. Structure of Noncommutative Solitons: Existence and Spectral Theory. Lett Math Phys 105, 1377–1398 (2015). https://doi.org/10.1007/s11005-015-0783-9

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  • DOI: https://doi.org/10.1007/s11005-015-0783-9

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