Local well-posedness of a coupled system of generalized Kadomtsev-Petviashvili II equations in anisotropic Gevrey spaces

In this study, we demonstrate that the coupled system of generalized Kadomtsev-Petviashvili II (KP-II) equations is locally well-posed in anisotropic Gevrey spaces G s 1 , s 2 γ 1 , γ 2 , ϱ ( R 2 ) . The conditions for the parameters s 1 , s 2 , and α are as follows: s 1 > − 3 α − 2 8 , s 2 ≥ 0 , and α ≥4. Our proof involves a suitable change of variables, and we present the results clearly. Additionally, we establish the regularity of the solutions in the time variable.