Blow-up and peakons for a higher-order $$\mu $$ μ -Camassa–Holm equation
Blow-up and peakons for a higher-order $$\mu $$ μ -Camassa–Holm equation
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DOI：
10.1007/s00028-022-00774-x
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发表时间：
2022-03
影响因子：
1.4
通讯作者：
Hao Wang;Ting Luo;Ying Fu;C. Qu
中科院分区：
文献类型：
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作者：
Hao Wang;Ting Luo;Ying Fu;C. Qu
本文提出了一个高阶Camassa-Holm方程，它是-Camassa-Holm方程的高阶推广，并保留了-Camassa-Holm方程的一些性质。我们首先证明了该方程存在由动量算符的格林函数给出的峰值行波解。证明了柯西问题在适当的Sobolev空间中的局部适定性。最后，研究了具有一定初始轮廓的解的爆破准则和破波机理。结果表明，所有的非线性，甚至一阶非线性，都可能对爆破产生影响。
This paper proposes a higher-order-Camassa–Holm equation, which is regarded as a higher-order extension of the-Camassa–Holm equation, and preserves some properties of the-Camassa–Holm equation. We first show that the equation admits the peaked traveling wave solution, which is given by a Green function of the momentum operator. Local well-posedness of the Cauchy problem in the suitable Sobolev space is established. Finally, the blow-up criterion and wave breaking mechanism for solutions with certain initial profiles are studied. It turns out that all the nonlinearities even the first-order nonlinearity may have the effect on the blow up.