Qualitative analysis for the new shallow -water model with cubic nonlinearity
Qualitative analysis for the new shallow -water model with cubic nonlinearity
复制标题
三次非线性新浅水模型的定性分析
DOI：
10.1016/j.jde.2020.04.003
复制
发表时间：
2020
影响因子：
2.4
通讯作者：
Guo Boling
中科院分区：
文献类型：
--
作者：
Mi Yongsheng;Liu Yue;Huang Daiwen;Guo Boling
本文考虑了一种新的具有立方非线性项的浅水模型，该模型允许单峰孤子和多峰孤子解，并包括修正的Camassa-Holm方程（又称Fokas-Olver-Rosenau-Qiao方程）和Novikov方程作为两种特殊情况。本文主要研究新浅水模型的柯西问题及其解的定性性质。我们首先建立了新浅水模型的Cauchy问题的局部适定性，然后推导出精确的爆破方案和爆破机制的某些初始配置文件的解决方案。此外，与解析的初始数据，我们表明，它的解决方案是解析的两个变量，全球的空间和局部的时间。最后，我们研究了新浅水模型柯西问题解的持久性。
Considered in this paper is the new shallow-water model with cubic nonlinearity, which admits the single peaked solitons and multi-peakon solutions, and includes both the modified Camassa-Holm equation (also called Fokas-Olver-Rosenau-Qiao equation) and the Novikov equation as two special cases. The main investigation is the Cauchy problem of the new shallow-water model with qualitative properties of its solutions. We first establish the local well-posedness for the Cauchy problem of the new shallow-water model, and then derive a precise blow-up scenario and the blow-up mechanisms for solutions with certain initial profiles. Moreover, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time. Finally, we investigate the persistence properties of the solution to the Cauchy problem of the new shallow-water model.