广义Davey-Stewartson方程的能量散射理论(英文)  

Energy Scattering for the Generalized Davey-Stewartson Equations

作　　者：郝成春[1] 

机构地区：[1]河北大学数学与计算机学院,河北保定071002

出　　处：《河北大学学报（自然科学版）》2002年第1期73-74,共2页Journal of Hebei University(Natural Science Edition)

基　　金：TheprojectissupportedbyNationalNaturalScienceFoundation(1990 10 0 7)

摘　　要：在浅水波理论中 ,通常的具有立方项的一维Schr dinger方程推广到二维的情形即是Davey Stewartson方程 .将此立方项推广到 p次幂非线性项的情形 ,进而考虑其初值在∑ (Rn) :={u∈H1(Rn) :|x|u∈L2 (Rn) }中的Cauchy问题的解的整体存在性及惟一性 。In the theory of water waves(esp.surface waves),the 2D generalization of the usual cubic 1D Schrdinger equation turns out to be the Davey Stewartson equation.The author generalizes its nonlinearity from the cubic case to the p th power cases.Through considering the Cauchy problem for the generalized Davey Stewartson equation in ∑(R n ):={ u∈H 1(R n ):|x|u∈L 2(R n )},the author obtains its scattering theory.Of course,the global existence and the uniqueness of the solution for the Cauchy problem are studied.

关 键 词：广义Davey-Stewartson方程 伪拱型守恒律 散射算子 SCHROEDINGER方程 能量散射理论 浅水波理论 CAUCHY问题 

分 类 号：O175.29[理学—数学]