论文标题
“好” Boussinesq方程：Riemann-Hilbert方法
The "good" Boussinesq equation: a Riemann-Hilbert approach
论文作者
论文摘要
我们为线上的“良好” Boussinesq方程式开发了反向散射变换形式主义。假设解决方案存在，我们表明它可以通过解决方案的$ 3 \ times 3 $矩阵Riemann-Hilbert问题来表示。 Riemann-Hilbert问题是根据两个反射系数提出的，它们的定义仅涉及初始数据，并且具有一种形式，可通过Deift-Zhou最陡峭的下降论证来评估长期渐近学。
We develop an inverse scattering transform formalism for the "good" Boussinesq equation on the line. Assuming that the solution exists, we show that it can be expressed in terms of the solution of a $3 \times 3$ matrix Riemann-Hilbert problem. The Riemann-Hilbert problem is formulated in terms of two reflection coefficients whose definitions involve only the initial data, and it has a form which makes it suitable for the evaluation of long-time asymptotics via Deift-Zhou steepest descent arguments.
