LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France.
Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow, 108840, Russia.
Phys Rev E. 2019 Jan;99(1-1):012210. doi: 10.1103/PhysRevE.99.012210.
We consider the long-time evolution of pulses in the Korteweg-de Vries equation theory for initial distributions which produce no soliton but instead lead to the formation of a dispersive shock wave and of a rarefaction wave. An approach based on Whitham modulation theory makes it possible to obtain an analytic description of the structure and to describe its self-similar behavior near the soliton edge of the shock. The results are compared with numerical simulations.
我们考虑 Korteweg-de Vries 方程理论中脉冲的长时间演化，对于产生不出孤子但会导致弥散激波和稀疏波形成的初始分布。基于 Whitham 调制理论的方法使得获得结构的解析描述并描述其在激波的孤子边缘附近的自相似行为成为可能。结果与数值模拟进行了比较。
