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Register a new userScattering theory for the Schrodinger-Debye System
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We study the Schrodinger-Debye system over $mathbb{R}^d$ iu_t+frac 12Delta u=uv,quad mu v_t+v=lambda |u|^2 and establish the global existence and scattering of small solutions for initial data in several function spaces in dimensions $d=2,3,4$. Moreover, in dimension $d=1$, we prove a Hayashi-Naumkin modified scattering result.
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In this paper, we study the solutions to the energy-critical quadratic nonlinear Schrodinger system in ${dot H}^1times{dot H}^1$, where the sign of its potential energy can not be determined directly. If the initial data ${rm u}_0$ is radial or non-radial but satisfies the mass-resonance condition, and its energy is below that of the ground state, using the compactness/rigidity method, we give a complete classification of scattering versus blowing-up dichotomies depending on whether the kinetic energy of ${rm u}_0$ is below or above that of the ground state.
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