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Dispersive estimates using scattering theory for matrix Hamiltonian equations

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  • We develop the techniques of [25] and [11] in order to derive dispersive estimates for a matrix Hamiltonian equation defined by linearizing about a minimal mass soliton solution of a saturated, focussing nonlinear Schrödinger equation

    $\i u_t + \Delta u + \beta (|u|^2) u = 0$
    $\u(0,x) = u_0 (x),$

    in $\mathbb{R}^3$. These results have been seen before, though we present a new approach using scattering theory techniques. In further works, we will numerically and analytically study the existence of a minimal mass soliton, as well as the spectral assumptions made in the analysis presented here.
    Mathematics Subject Classification: Primary: 35B35, 35P10.


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