We consider the initial value problem (IVP) associated to a coupled system of Kawahara/KdV type equations. We prove the well-posedness results for given data in a Gevrey spaces. The proof relies on estimates in space-time norms adapted to the linear part of the equations. In particular, estimates in Bourgain spaces are proven for the linear and nonlinear terms of the system and the main result is obtained by a contraction principle. The class of system in view contains a number of systems arising in the modeling of waves in fluids, stability and instability of solitary waves and models for wave propagation in physical systems where both nonlinear and dispersive effects are important. The techniques presented in this work were based in Grujić and Kalisch, who studied the Gevrey regularity for a class of water-wave models and the well-posedness of a IVP associated to a general equation, whose the initial data belongs to Gevrey spaces.

我们考虑与Kawahara / KdV型方程的耦合系统相关的初始值问题（IVP）。我们证明了Gevrey空间中给定数据的适定性结果。证明依赖于适应方程线性部分的时空范数的估计。特别是，证明了布尔加因空间中系统线性和非线性项的估计，并且主要结果是通过收缩原理获得的。可见的系统类别包括许多在流体中的波建模，孤立波的稳定性和不稳定性以及在非线性和色散效应均很重要的物理系统中传播的波模型。这项工作中介绍的技术基于Grujić和Kalisch，