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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Technology and Business University, Beijing, 100048, People’s Republic of China

    Yu-Lan Ma

  2. School of Computer Science and Engineering, Beijing Technology and Business University, Beijing, 100048, People’s Republic of China

    Bang-Qing Li

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  1. Yu-Lan Ma
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B-QL: Data check, visualization, software, writing—reviewing and editing. Y-LM: Conceptualization, methodology, writing—original draft preparation, corresponding author.

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Correspondence to Bang-Qing Li.

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Ma, YL., Li, BQ. Interaction Behaviors Between Solitons, Breathers and Their Hybrid Forms for a Short Pulse Equation. Qual. Theory Dyn. Syst. 22, 146 (2023). https://doi.org/10.1007/s12346-023-00844-6

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