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.