On the initial value problem for a class of nonlinear integral evolution equations including the sine-Hilbert equation
On the initial value problem for a class of nonlinear integral evolution equations including the sine-Hilbert equation
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DOI：
10.1063/1.527763
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发表时间：
1987-10
影响因子：
1.3
通讯作者：
P. Santini;M. Ablowitz;A. Fokas
中科院分区：
文献类型：
--
作者：
P. Santini;M. Ablowitz;A. Fokas
提出了求解一类线性初始值衰减的非线性奇异积分演化方程的方法。潜在的散射问题是矩阵黎曼-希尔伯特问题。散射分析表明光谱是纯离散的。一个应用是所谓的正弦希尔伯特方程 Hθt =−c sin θ，其中 c 是常数，H 表示希尔伯特变换。
A method for solving a class of nonlinear singular integral evolution equations for decaying initial values on the line is presented. The underlying scattering problem is a matrix Riemann–Hilbert problem. Scattering analysis shows that the spectrum is purely discrete. An application is to the so‐called sine–Hilbert equation Hθt =−c sin θ, where c is a constant and H denotes the Hilbert transform.