Zobrazeno 1 - 10
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pro vyhledávání: '"Xu, Chengbin"'
Autor:
Guzmán, Carlos M., Xu, Chengbin
The purpose of this work is to study the $3D$ energy-critical inhomogeneous generalized Hartree equation $$ i\pa_tu+\Delta u+|x|^{-b}(I_\alpha\ast|\cdot|^{-b}|u|^{p})|u|^{p-2}u=0,\;\ x\in\R^3, $$ where $p=3+\alpha-2b$. We establish global well-posedn
Externí odkaz:
http://arxiv.org/abs/2305.00972
Publikováno v:
In Journal of King Saud University - Computer and Information Sciences October 2024 36(8)
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 January 2025 541(1)
In this paper, we study the dynamics behavior of the NLS system with three waves interaction in the energy space $H^1(\mathbb{R}^5) \times H^1(\mathbb{R}^5)\times H^1(\mathbb{R}^5) $. Inspired by B. Dodson and J. Murphy in \cite{Dodson2018}, we estab
Externí odkaz:
http://arxiv.org/abs/2201.09408
In this article, we consider the dynamics of the energy-critical quadratic nonlinear Schr\"odinger system $\[ \left\{ \begin{aligned} & i u^1_t + \kappa_1 \Delta u^1 = -\overline{u^2}u^3, \\ & i u^2_t + \kappa_2 \Delta u^2 = -\overline{u^1}u^3, \\ &
Externí odkaz:
http://arxiv.org/abs/2110.05277
Publikováno v:
In Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena June 2024 183
In this article, we aim to study the scattering of the solution to the focusing inhomogeneous nonlinear Schr\"odinger equation with a potential of form \begin{align*} i\partial_t u+\Delta u- Vu=-|x|^{-b}|u|^{p-1}u \end{align*} in the energy space $H^
Externí odkaz:
http://arxiv.org/abs/2107.06094
In this paper, we study the solutions to the energy-critical quadratic nonlinear Schr\"odinger system in ${\dot H}^1\times{\dot H}^1$, where the sign of its potential energy can not be determined directly. If the initial data ${\rm u}_0$ is radial or
Externí odkaz:
http://arxiv.org/abs/2107.05299
In this paper, we prove a limiting absorption principle for high-order Schr\"odinger operators with a large class of potentials which generalize some results by A. Ionescu and W. Schlag. Our main idea is to handle the boundary operators by the restri
Externí odkaz:
http://arxiv.org/abs/2106.14242
Autor:
Xu, Chengbin
In this paper, we study the long-time behavior of global solutions to the Schr\"odinger-Choquard equation $$i\partial_tu+\Delta u=-(I_\alpha\ast|\cdot|^b|u|^{p})|\cdot|^b|u|^{p-2}u.$$ Inspired by Murphy, who gave a simple proof of scattering for the
Externí odkaz:
http://arxiv.org/abs/2104.09756