耦合Schrdinger-KdV方程组Cauchy问题的适定性  

Well-posedness of the Cauchy Problem for the Coupled System of the Schrdinger-KdV Equations

作　　者：郭柏灵[1] 苗长兴[1] 

机构地区：[1]北京应用物理与计算数学研究所

出　　处：《数学学报（中文版）》1998年第6期1295-1302,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金;中国工程物理研究院基金

摘　　要：本文研究了耦合Schrodinger－KdV方程组的Cauchy问题，此耦合方程组刻化了一维Langmuir和离子声波相互作用的非线性动力学行为．本文建立了此问题在Hk×Hk中的整体适定性理论（k∈Z+）．This paper is devoted to the study of the Cauchy problem for the coupled system of the Schrodinger-KdV equations which describes the nonlinear dynamics of the one-dimensional Langmuir and ion-acoustic waves. Global well-posedness of the problem is established in the space Hk x Hk (k ∈ Z+), the first and second component of which correspond to the electric field of the Langmuir oscillations and low-frequency density perturbation respectively.

关 键 词：适定性 S-KdV方程组 初值问题 薛定谔方程 

分 类 号：O175.29[理学—数学] O175.24[理学—基础数学]