Collisions and fusion of one- and two-dimensional solitons driven by potential troughs in the cubic–quintic nonlinear Schrödinger equations

We study the formation and collision of 1D (one-dimensional) and 2D (two-dimensional) Gaussian-shaped and flat-top (FT) solitons in the framework of the nonlinear Schrödinger equation with the cubic–quintic nonlinearity and two intersecting potential troughs. We find that Gaussian–Gaussian and Gaussian–FT collisions between the solitons, steered by the troughs, are quasi-elastic, while the collisions between FT solitons may be either quasi-elastic or inelastic, in the form of merger into a single FT soliton, thus spontaneously breaking the symmetry between the steering troughs. The Gaussian–FT collisions, being overall quasi-elastic, generate weak radiation fields.