Blow-up and peakons for a higher-order μ -Camassa–Holm equation
Blow-up and peakons for a higher-order μ -Camassa–Holm equation
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发表时间：
2022
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通讯作者：
Hao-Tian Wang;Ting Luo;Ying Fu;C. Qu
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作者：
Hao-Tian Wang;Ting Luo;Ying Fu;C. Qu
。本文提出了一个高阶μ-Camassa-Holm方程，它是μ-Camassa-Holm方程的高阶推广，保留了μ-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fi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，研究了具有一定初值问题解的爆破准则和破波机制。结果表明，所有的非线性，甚至fi的一阶非线性，都可能对爆破产生影响。
. This paper proposes a higher-order μ -Camassa–Holm equation, which is regarded as a higher-order extension of the μ -Camassa–Holm equation, and preserves some properties of the μ -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.