The Inverse Scattering Transform for the Benjamin‐Ono Equation—A Pivot to Multidimensional Problems
The Inverse Scattering Transform for the Benjamin‐Ono Equation—A Pivot to Multidimensional Problems
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DOI：
10.1002/sapm19836811
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发表时间：
1983-02
影响因子：
2.7
通讯作者：
A. Fokas;M. Ablowitz
中科院分区：
文献类型：
--
作者：
A. Fokas;M. Ablowitz
与Benjamin‐Ono方程相关的初值问题通过逆散射变换的适当扩展线性化。本质是一个相关的非局部黎曼-希尔伯特问题的初始散射数据的制定和解决方案。孤子被赋予了明确的频谱特征。纯孤子解是通过求解一个线性代数系统得到的，该系统的系数线性地依赖于[INLINEEQUATION]，[INLINEEQUATION]。
The initial value problem associated with the Benjamin‐Ono equation is linearized by a suitable extension of the inverse scattering transform. Essential is the formulation and solution of an associated nonlocal Riemann‐Hilbert problem in terms of initial scattering data. Solitons are given a definitive spectral characterization. Pure soliton solutions are obtained by solving a linear algebraic system whose coefficients depend linearly on [INLINEEQUATION], [INLINEEQUATION].