Interaction Behaviors Between Solitons, Breathers and Their Hybrid Forms for a Short Pulse Equation

In this article, we investigate the dynamical interaction behavior of a short pulse equation in optical fibers with fast-varying packets. We systematically unearth the interaction dynamics between solitons, breathers, and their hybrid forms. Using the bilinear method, we explicitly calculate the first- to fourth-order solutions. We categorize the solutions into three classes based on their dispersion coefficients: stripe-loop-like soliton, breather, and their hybrid form. We observe the existence of bright and dark solitons. Additionally, a breather may consist of periodical peak-trough waves and periodical kink-loop-like waves. As the order of the solutions increases, there are abundant and complicated interaction behaviors for the solitons, breathers, and their hybrid forms due to these rich patterns.