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

• Published in: Qualitative theory of dynamical systems Vol. 22; no. 4
• Main Authors: Ma, Yu-Lan, Li, Bang-Qing
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2023; Springer Nature B.V
• Subjects: Breathers; Difference and Functional Equations; Dynamical Systems and Ergodic Theory; Mathematical analysis; Mathematics; Mathematics and Statistics; Optical fibers; Short pulses; Solitary waves; Bilinear method; Short pulse equation (SPE); Stripe-loop-like soliton; Breather; Hybrid form; Interaction behaviors
• ISSN: 1575-5460; 1662-3592
• DOI: 10.1007/s12346-023-00844-6

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.