| 广义Davey-Stewartson方程的能量散射理论 |
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| 引用本文： | 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. DOI: 10.3969/j.issn.1000-1565.2002.01.018 |
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| 作者姓名： | 郝成春 |
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| 作者单位： | 河北大学数学与计算机学院,河北,保定,071002 |
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| 基金项目： | TheprojectissupportedbyNationalNaturalScienceFoundation(1990 10 0 7) |
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| 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.
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| 关 键 词： | 广义Davey-Stewartson方程 伪拱型守恒律 散射算子 |
Energy Scattering for the Generalized Davey-Stewartson Equations |
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| Abstract. Energy Scattering for the Generalized Davey-Stewartson Equations[J]. Journal of Hebei University (Natural Science Edition), 2002, 22(1): 73-74. DOI: 10.3969/j.issn.1000-1565.2002.01.018 |
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| Authors: | Abstract |
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| Abstract: | In the theory of water waves(esp. Surface waves), the 2D generalization of the usual cubic 1DSchrodinger 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-Stewartson 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. |
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| Keywords: | generalized Davey Stewartson equation pseudo conformally invariant conservation law scattering operator |
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