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Interaction with an obstacle in the 2d focusing nonlinear Schrodinger equation

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 Added by Kai Yang
 Publication date 2021
and research's language is English




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We present a numerical study of solutions to the $2d$ focusing nonlinear Schrodinger equation in the exterior of a smooth, compact, strictly convex obstacle, with Dirichlet boundary conditions with cubic and quintic powers of nonlinearity. We study the effect of the obstacle on solutions traveling toward the obstacle at different angles and with different velocities. We introduce a concept of weak and strong interactions and show how the obstacle changes the overall behavior of solutions.



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72 - Chengbin Xu 2021
In this paper, we study the long-time behavior of global solutions to the Schrodinger-Choquard equation $$ipartial_tu+Delta u=-(I_alphaast|cdot|^b|u|^{p})|cdot|^b|u|^{p-2}u.$$ Inspired by Murphy, who gave a simple proof of scattering for the non-radial inhomogeneous NLS, we prove scattering theory below the ground state for the intercritical case in energy space without radial assumption.
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185 - Yongming Luo 2021
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