论文标题
Whitham-Boussinesq系统的孤独波碰撞
Solitary wave collisions for Whitham-Boussinesq systems
论文作者
论文摘要
这项工作涉及两种Whitham-Boussinesq型模型的孤子型数值解决方案。使用迭代性牛顿型和延续方法计算孤立波。该方法使我们能够以较大的幅度和速度接近奇异极限的速度来计算孤立波。这些孤立的波是作为初始数据设置的，并且考虑了两个系统的超车碰撞。我们表明，这两个系统都满足了两索碰撞的几何拉克斯分类。数值证据表明，其中一个系统还基于初始孤立波幅度的比率，与LAX预测的范围不同，该系统也接受了代数宽松类别。但是，我们表明第二个系统不可能进行这种分类。
This work concerns soliton-type numerical solutions for two Whitham-Boussinesq-type models. Solitary waves are computed using an iterative Newton-type and continuation methods with high accuracy. The method allow us to compute solitary waves with large amplitude and speed close to the singular limit. These solitary waves are set as initial data and overtaking collisions are considered for both systems. We show that both system satisfy the geometric Lax-categorization of two-soliton collision. Numerical evidences indicate that one of the systems also admits an algebraic Lax-categorization based on the ratio of the initial solitary wave amplitudes with a different range from the one predicted by Lax. However, we show that such categorization is not possible for the second system.
