Exact analytical Helmholtz bright and dark solitons

In this paper, we have presented exact analytical Helmholtz bright and dark soliton solutions for a Kerr nonlinearity. Simulations verify that these solutions are both robust and act as attractors in nonlinear beam dynamics. Results dealing with the coherent interaction of Helmholtz bright solitons have also been presented, for the first time. These considerations extend previous(paraxial) studies that are only valid for vanishingly small interaction angles.