吉林大学学报（理学版）2026，Vol.64Issue(3)：475-482,8.DOI:10.13413/j.cnki.jdxblxb.2025235
高维含时势导数非线性Schrödinger系统的渐近行为
Asymptotic Behavior of Derivative Nonlinear Schrödinger Systems with Time-Dependent Potentials in High-Dimensional Space
摘要
Abstract
We considered the initial problem of derivative Schrödinger systems with time-dependent potentials and quadratic nonlinearities in high-dimensional(d≥3)space.Firstly,under the condition of mass resonance,we obtained the priori estimates of solutions to the systems by using the tools such as energy inequalities and embedding theorems.Secondly,we proved the global existence of solutions for the nonlinear Schrödinger systems with small initial value by using priori estimates.Finally,by constructing auxiliary functions,we demonstrate that the solutions to the systems are asymptotically free under the condition of mass resonance.关键词
导数非线性Schrödinger系统/含时势函数/质量共振关系/渐近行为Key words
derivative nonlinear Schrödinger system/time-dependent potential/mass resonance relation/asymptotic behavior分类
数理科学引用本文复制引用
徐小迪,李春花..高维含时势导数非线性Schrödinger系统的渐近行为[J].吉林大学学报（理学版）,2026,64(3):475-482,8.基金项目
国家自然科学基金(批准号:12361051)和吉林省教育厅项目(批准号:JJKH20250396KJ). （批准号:12361051）
