广义Davey-Stewartson方程的能量散射理论

doi:10.3969/j.issn.1000-1565.2002.01.018

河北大学学报(自然科学版) ›› 2002, Vol. 22 ›› Issue (1): 73-74.DOI: 10.3969/j.issn.1000-1565.2002.01.018

广义Davey-Stewartson方程的能量散射理论

郝成春

河北大学数学与计算机学院,河北,保定,071002

出版日期:2002-02-25 发布日期:2002-02-25
基金资助:
国家自然科学基金

Energy Scattering for the Generalized Davey-Stewartson Equations

Online:2002-02-25 Published:2002-02-25

摘要/Abstract

摘要： 在浅水波理论中,通常的具有立方项的一维Schrodinger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,得到该方程的散射理论.

关键词: 广义Davey-Stewartson方程, 伪拱型守恒律, 散射算子

Abstract: In the theory of water waves(esp. Surface waves), the 2D generalization of the usual cubic 1D Schrodinger equation tums 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-Stew artson equation in ∑(Rn): = { u ∈ H1 (Rn): ｜ x ｜ u ∈ L2 (Rn)} , the author obtains its scattering theory. Of course, the global existence and the uniqueness of the solution for the Cauchy problem are studied.

Key words: generalized Davey-Stewartson equation, pseudo conformally invariant conservation law, scatter ing operator

中图分类号:

O175.29

郝成春. 广义Davey-Stewartson方程的能量散射理论[J]. 河北大学学报(自然科学版), 2002, 22(1): 73-74.

广义Davey-Stewartson方程的能量散射理论

Energy Scattering for the Generalized Davey-Stewartson Equations

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