TY - JOUR TI - Structure and dynamics of noncommutative solitons DO - https://doi.org/doi:10.7282/T3765CS3 PY - 2014 AB - We consider the Schrödinger equation with a Hamiltonian given by a second order o 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 prove pointwise in time decay estimates, with the optimal decay rate t−1 log−2 t generically. We use a novel technique involving generating functions of orthogonal polynomials to achieve these estimates. We construct a ground state soliton for this equation and analyze its properties. In particular we arrive at ∞ and 1 estimates as well as a quasi-exponential spatial decay rate. We completely determine the spectrum of the associated linearized Hamiltonian and prove the optimal decay rate of t−1 log−2 t for the associated time decay estimate. These results are to appear in forthcoming papers KW - Physics and Astronomy KW - Noncommutative differential geometry KW - Spectral theory (Mathematics) LA - eng ER -