Evolution of initial discontinuities in the Riemann problem for the Jaulent–Miodek equation with positive dispersion
作者：
Highlights：
• As we know, since the JM system with positive dispersion is modulationally unstable, the corresponding behaviors of Riemann problem are more complicated than the stable JM system. This manuscript has made the complete classification for initial discontinuities in Riemann problems for the JM system, and applied the JM-Whitham system to describe the dispersive effect in two physical model cases, the dam breaking problem and piston problem.
• Riemann problem plays a very basic role in the theoretical study of partial differential equations. In my opinion, the authors succeed in giving a convincing answer to the evolution of initial discontinuities in the Riemann problem of JM equations using Whitham theory. The method used here is systematic.
摘要
•As we know, since the JM system with positive dispersion is modulationally unstable, the corresponding behaviors of Riemann problem are more complicated than the stable JM system. This manuscript has made the complete classification for initial discontinuities in Riemann problems for the JM system, and applied the JM-Whitham system to describe the dispersive effect in two physical model cases, the dam breaking problem and piston problem.•Riemann problem plays a very basic role in the theoretical study of partial differential equations. In my opinion, the authors succeed in giving a convincing answer to the evolution of initial discontinuities in the Riemann problem of JM equations using Whitham theory. The method used here is systematic.
论文关键词：
论文评审过程：Received 21 July 2021, Revised 30 November 2021, Accepted 10 December 2021, Available online 22 December 2021, Version of Record 22 December 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126869
