Multidimensional optical pulses in non-resonant quadratic materials

In a one-dimensional nonresonant quadratic material, the evolution of the slowly-varying envelope of the optical pulse was found by the nonlinear Schrodinger equation (NLS). The NLS equation is also a centrally important equation in other areas such as fluid dynamics. However, it is well known that (1+1)-dimensional structures propagating in a multidimensional medium may be unstable with respect to transverse modulations. As a consequence, pulse dynamics in a multidimensional medium cannot be reduced to simple one-dimensional systems. When studying the modulation of a wave packet in a multidimensional dispersive medium, generalized NLS systems with coupling to a mean term (NLSM) are known to appear in various physical situations.