Direct Scattering for the Benjamin-Ono Equation with Rational Initial Data

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• 作者：Peter D. Miller and Alfredo N. Wetzel
• 刊名：Studies in Applied Mathematics
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：137
• 期：1
• 页码：53-69
• 全文大小：212K
• ISSN：1467-9590

文摘

We compute the scattering data of the Benjamin–Ono equation for arbitrary rational initial conditions with simple poles. Specifically, we obtain explicit formulas for the Jost solutions and eigenfunctions of the associated spectral problem, yielding an Evans function for the eigenvalues and formulas for the phase constants and reflection coefficient.