  The nonlinear dynamics of an obliquely oriented wave packet at sea surface is
studied both analytically and numerically for various initial parameters of the
packet, in connection with the problem of oceanic rogue waves. In the framework
of Gaussian variational ansatz applied to the corresponding (1+2D) hyperbolic
nonlinear Schr\"odinger equation, a simplified Lagrangian system of
differential equations is derived, which determines the evolution of
coefficients of the real and imaginary quadratic forms appearing in the
Gaussian. This model provides a semi-quantitative description for the process
of nonlinear spatio-temporal focusing, which is one of the most probable
mechanisms of rogue wave formation in random wave fields. The system is
integrated in quadratures, which fact allows us to understand qualitative
differences between the linear and nonlinear regimes of the focusing of wave
packet. Comparison of the Gaussian model predictions with results of direct
numerical simulation of fully nonlinear long-crested water waves is carried
out.
