A variational method for extended nonlinear Schrِdinger systems

We develop a variational procedure for solving nonlinear Schrödinger equations in the form i∂z u+Δu+q∣u∣2 u+F(u)=0, where F(u) is an arbitrary function of u, being perturbative or not. This method provides a general dynamical system describing the typical length scale of localized solutions u and it includes a relation for the power lost by these solutions in dissipative systems. The complete set of dynamical equations is then applied to models describing the propagation of high-power beams in gases, which involve saturating nonlinearities, multiphoton sources and nonlinear dissipation as well. Theoretical results are confronted with numerical simulations.