论文标题
具有科里奥利效应的广义旋转 - 木马方程的行进波
Traveling waves of a generalized Rotation-Camassa-Holm equation with the Coriolis effect
论文作者
论文摘要
在本文中，我们分析了广义旋转 - 卡马萨 - 霍尔姆方程的动力学，这是通过地球旋转引起的coriolis效应增强的$θ$方程。广义的旋转 - 卡马萨 - 霍尔姆方程（称为旋转 - $θ$方程）是对模型家族的概括（包括$θ= \ frac {1} {1} {3} $的旋转 - 卡马萨 - 霍尔姆方程，用于$ univation-camassa-holm方程的$ to $ the Rotise = 1 $ usteris = 1 $ usteris Proceatiation ddp） $θ= \ frac {1} {4} $）。我们的研究是通过分叉方法和动力学系统定性理论进行的。不仅显示了光滑的单生波解，周期性波解决方案，还显示了山峰和周期性的Pearmon溶液。所选的值$θ$，允许我们评估经典$θ$ - 方程与旋转 - $θ$方程之间的行为差异。我们得出的结论是，科里奥利效应确实会影响波动波解决方案。我们总结了第4节中三个定理中波的分叉和显式表达式。一个结论结束了论文。
In this paper, we analyze the dynamics of a generalized Rotation-Camassa-Holm equation, which is the $θ$-equation augmented with the Coriolis effect, induced by the earth rotation. The generalized Rotation-Camassa-Holm equation (named as Rotation-$θ$ equation) is a generalization of a family of models (including the Rotation-Camassa-Holm equation for $θ=\frac{1}{3}$, asymptotic Rotation-Camassa-Holm equation for $θ=1$ and the Rotation-Degasperis-Procesi (DP) equation for $θ=\frac{1}{4}$). Our study is conducted via the bifurcation method and qualitative theory of dynamical systems. The existence of not only smooth solitary wave solutions, periodic wave solutions, but also peakons and periodic peakon solutions is shown. The chosen values $θ$, allow us to assess the difference in behavior between the classical $θ$-equation and the Rotation-$θ$ equation. We conclude that the Coriolis effect does affect the traveling wave solutions. We summarize the bifurcations and explicit expressions of waves solutions in three theorems in Section 4. A conclusion ends the paper.
