Asymptotic stability and completeness in 2D nonlinear Schrodinger equation

Mathematics;Partial Differential Equations;Schrödinger Equation;Nonlinear;Completeness;Asymptotic Stability

Skulkhu, Ruth

关键词: Mathematics;    Partial Differential Equations;    Schrödinger Equation;    Nonlinear;    Completeness;    Asymptotic Stability;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/32082/Skulkhu_Ruth.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

In this thesis we obtained new results on the asymptotic stability of ground states of thenonlinear Schrödinger equation in space dimension two. Under our hypotheses, the resultactually shows asymptotic completeness in the regime of small initial data, i.e. any smallinitial data evolves into a superposition of a solitary wave (ground state) and a radiativepart that decays in time.