Structure of Noncommutative Solitons: Existence and Spectral Theory

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.

18 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1411.4298

References in corpus (6)

• Dispersion Estimates for One-dimensional Discrete Schrödinger and Wave Equations
• Multi-Component NLS Models on Symmetric Spaces: Spectral Properties versus Representations Theory
• Solitons in one-dimensional nonlinear Schrödinger lattices with a local inhomogeneity
• On asymptotic stability of standing waves of discrete Schrödinger equation in $\mathbb{Z}$
• Noncommutative Solitons
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Cited by in corpus (5)

• Jacobi Polynomials, Bernstein-type Inequalities and Dispersion Estimates for the Discrete Laguerre Operator
• Dynamics of Noncommutative Solitons I: Spectral Theory and Dispersive Estimates
• Heat kernels of the discrete Laguerre operators
• Dispersion Estimates for the Discrete Laguerre Operator
• Dynamics of Noncommutative Solitons II: Spectral Theory, Dispersive Estimates and Stability