Propagation of Cartesian beams in nonlocal nonlinear media

We introduce a very general self-trapped beam solution of the Snyder-Mitchell linear model in Cartesian coordinates. We name such a field a self-trapped Cartesian beam (CB) which is characterized by two parameters. The complex amplitude of the self-trapped CBs is described by the product of the parabolic cylinder functions and the Gaussian function. The self-trapped standard, elegant, and generalized Hermite-Gaussian beams can be obtained by treating them as the special cases of the self-trapped CBs.