论文标题
分数Korteweg--de Vries和Degasperis-Procesi方程的最高波
Highest waves for fractional Korteweg--De Vries and Degasperis--Procesi equations
论文作者
论文摘要
我们研究了一类分数korteweg-de vries和分数degasperis-procesi方程的行进波，其参数化的傅立叶乘数乘以$ -s \ in（-1，0）$。对于这两个方程式，都存在局部分析分支分支，这些分支从恒定溶液的曲线中产生，包括光滑，均匀且周期性的行进波。本地分支扩展到全局解决方案曲线。在限制下，我们发现了最高的，尖锐的旅行波解决方案，并证明其在浪尖上获得的最佳$ S $-Hölder规律性。
We study traveling waves for a class of fractional Korteweg--De Vries and fractional Degasperis--Procesi equations with a parametrized Fourier multiplier operator of order $-s \in (-1, 0)$. For both equations there exist local analytic bifurcation branches emanating from a curve of constant solutions, consisting of smooth, even and periodic traveling waves. The local branches extend to global solution curves. In the limit we find a highest, cusped traveling-wave solution and prove its optimal $s$-Hölder regularity, attained in the cusp.
