论文标题
通过darboux转换在稀有波浪背景上的孤子
Solitons on the rarefactive wave background via the Darboux transformation
论文作者
论文摘要
在许多非线性进化方程中，包括梯级初始数据（包括Korteweg-de Vries（KDV）方程的经典示例），产生了稀有波浪和色散冲击波。当将单个波浪注入类似阶梯的初始数据时，它要么在背景上传输，要么被困在稀有波浪中。我们表明，可以通过使用darboux转换来获得kdv方程的传输孤子。另一方面，无法使用Darboux转换获得无捕获的孤子，我们通过数值模拟显示，捕获的孤子在稀有波浪的长期动力学中消失了。
Rarefactive waves and dispersive shock waves are generated from the step-like initial data in many nonlinear evolution equations including the classical example of the Korteweg-de Vries (KdV) equation. When a solitary wave is injected on the step-like initial data, it is either transmitted over the background or trapped in the rarefactive wave. We show that the transmitted soliton can be obtained by using the Darboux transformation for the KdV equation. On the other hand, no trapped soliton can be obtained by using the Darboux transformation and we show with numerical simulations that the trapped soliton disappears in the long-time dynamics of the rarefactive wave.
