Ablowitz Mark J, Cole Justin T, Rumanov Igor
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309, USA.
Proc Math Phys Eng Sci. 2020 Aug;476(2240):20200300. doi: 10.1098/rspa.2020.0300. Epub 2020 Aug 5.
The semi-classical Korteweg-de Vries equation for step-like data is considered with a small parameter in front of the highest derivative. Using perturbation analysis, Whitham theory is constructed to the higher order. This allows the order one phase and the complete leading-order solution to be obtained; the results are confirmed by extensive numerical calculations.
考虑具有最高阶导数前带小参数的阶梯状数据的半经典科特韦格 - 德弗里斯方程。通过微扰分析，将惠特姆理论构建到更高阶。这使得能够获得一阶相位和完整的主导阶解；大量数值计算证实了这些结果。
