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Structure of noncommutative solitons: existence and spectral theory. (English) Zbl 1327.35328

Summary: 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.

MSC:

35Q40 PDEs in connection with quantum mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)
39A05 General theory of difference equations
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