Breather-to-soliton transitions and nonlinear wave interactions for the nonlinear Schrödinger equation with the sextic operators in optical fibers

We find that the sextic nonlinear Schrödinger (NLS) equation admits breather-to-soliton transitions. With the Darboux transformation, analytic breather solutions with imaginary eigenvalues up to the second order are explicitly presented. The condition for breather-to-soliton transitions is explicitly presented and several examples of transitions are shown. Interestingly, we show that the sextic NLS equation admits not only the breather-to-bright-soliton transitions but also the breather-to-dark-soliton transitions. We also show the interactions between two solitons on the constant backgrounds, as well as between breather and soliton.