arXiv math/07024652007-02math.APmath-phmath.MP

Slow soliton interaction with delta impurities

Justin Holmer, Maciej Zworski

英文摘要：

We study the Gross-Pitaevskii equation with a delta function potential, $ q δ_0 $, where $|q|$ is small, and analyze the solutions for which the initial condition is a soliton with initial velocity $v_0$. We show that up to time $ (|q| + v_0^2)^{-\frac12} \log(1/|q|) $ the bulk of the solution is a soliton evolving according to the classical dynamics of a natural effective Hamiltonian, $ (ξ^2 + q \sech^2 (x))/2 $.

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