We consider the Cauchy problem of the fifth‐order Korteweg–de Vries (KdV) equations without nonlinear dispersive term

$${\partial }_{t}u-{\partial }_x^{5}u+b_{0}u{\partial }_{x}u+b_1{\partial }_x{({\partial }_{x}u)}^2=0,(t,x)\in ℝ\times 𝕋.$$ (0.1)

中文翻译：

---

一类无非线性色散项的周期五阶Korteweg-de Vries方程的局部适定性

我们考虑没有非线性色散项的五阶Korteweg-de Vries（KdV）方程的柯西问题

$${\partial }_{Ť}ü-{\partial }_X^5ü+b_0ü{\partial }_Xü+b_{\mathrm{1个}}{\partial }_X{（{\partial }_Xü）}^{\mathrm{2个}}=0，（Ť，X）\in ℝ\times 𝕋。$$ （0.1）