The scattering transform for the Benjamin-Ono equation
The scattering transform for the Benjamin-Ono equation
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Benjamin-Ono 方程的散射变换
DOI：
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发表时间：
1990
期刊：
影响因子：
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通讯作者：
M. Wickerhauser
中科院分区：
文献类型：
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作者：
R. Coifman;M. Wickerhauser
本文用构造性方法研究了Benjamin-Ono方程的谱理论。由于以前使用的线性化级数是奇异的，他们用有限秩重整化得到的改进级数代替它。这就引入了额外的散射数据，这被证明是依赖于一个单一的功能，虽然不是通常的。然后，他们证明了连续的直接和逆散射变换定义的改进系列小复杂的潜力。
The authors use constructive methods to investigate the spectral theory of the Benjamin-Ono equation. Since the linearization series used previously is singular, they replace it with an improved series obtained by finite-rank renormalization. This introduces additional scattering data, which are shown to be dependent upon a single function, though not the usual one. They then prove the continuity of the direct and inverse scattering transforms defined by the improved series for small complex potentials.