AI 中文总结
研究三维非线性薛定谔方程的散射及逆散射问题，通过大数据散射行为来唯一确定方程中的非齐次项\(a(x)\)，为相关方程研究提供新视角与方法。
AI 中文摘要
本文研究形如\(\mathrm{i}\partial_t u + \Delta u = a(x)|u|^2u\)的三维非线性薛定谔方程的散射和逆散射问题。对于合适类别的\(a(x)\)，此类方程是整体适定的且有大数据散射理论。我们证明大数据散射行为唯一确定非齐次项\(a(x)\)。
英文摘要
In this article, we study scattering and inverse scattering problems for 3D nonlinear Schrödinger equations of the form, $$ \mathrm{i}\partial_t u + Δu = a(x)|u|^2u.$$ For $a(x)$ in a suitable class, such equations are globally well-posed and admit a large-data scattering theory. In this work, we prove that the large-data scattering behavior uniquely determines the inhomogeneity $a(x)$.
Comments14 pages. Major revision of v1
