Long time existence for a two-dimensional strongly dispersive Boussinesq system

We prove a long time existence result for the solutions of two-dimensional Boussinesq system modeling propagation long, weakly nonlinear water waves. This is exceptional in sense that it only linearly well-posed (abcd) family systems whose eigenvalues linearized have nontrivial zeroes. new difficulty solved by use “good unknowns” and normal form techniques.