We prove several dispersive estimates for the linear part of the Full Dispersion Kadomtsev–Petviashvili introduced by David Lannes to overcome some shortcomings of the classical Kadomtsev–Petviashvili equations. The proof of these estimates combines the stationary phase method with sharp asymptotics on asymmetric Bessel functions, which may be of independent interest. As a consequence, we prove that the initial value problem associated to the Full Dispersion Kadomtsev–Petviashvili is locally well-posed in \(H^s(\mathbb R^2)\), for \(s>\frac{7}{4}\), in the capillary-gravity setting.

中文翻译：

---

全色散KP方程的色散估计

我们证明了David Lannes为克服经典Kadomtsev-Petviashvili方程的一些缺点而引入的全色散Kadomtsev-Petviashvili的线性部分的几个色散估计。这些估计的证明将固定相方法与不对称贝塞尔函数的尖锐渐近性结合在一起，这可能是独立引起关注的。结果，我们证明了与全分散Kadomtsev–Petviashvili相关的初值问题在\（H ^ s（\ mathbb R ^ 2）\）中对于\（s> \ frac {7} {4} \），在毛细管重力设置中。