## 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

### Keywords:

noncommutative soliton; spectral theory; NLS; DNLS
Full Text:

### References:

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