Structure of Noncommutative Solitons: Existence and Spectral Theory

August J. Krueger, Avy Soffer

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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 $${\ell^{\infty}}$$ℓ∞ and $${\ell^{1}}$$ℓ1 estimates as well as a quasi-exponential spatial decay rate.

Original languageEnglish (US)
Pages (from-to)1377-1398
Number of pages22
JournalLetters in Mathematical Physics
Issue number10
StatePublished - Oct 14 2015

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • DNLS
  • NLS
  • noncommutative soliton
  • spectral theory


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