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Article

Peakons and Persistence Properties of Solution for the Interacting System of Popowicz

by
Yaohong Li
* and
Chunyan Qin
Research Center of Dynamical Systems and Control, Suzhou University, Suzhou 234000, China
*
Author to whom correspondence should be addressed.
Mathematics 2023, 11(16), 3529; https://doi.org/10.3390/math11163529
Submission received: 22 June 2023 / Revised: 5 August 2023 / Accepted: 10 August 2023 / Published: 15 August 2023
(This article belongs to the Section E4: Mathematical Physics)
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Abstract

This paper focuses on a two-component interacting system introduced by Popowicz, which has the coupling form of the Camassa–Holm and Degasperis–Procesi equations. Using distribution theory, single peakon solutions and several double peakon solutions of the system are described in an explicit expression. Moreover, dynamic behaviors of several types of double peakon solutions are illustrated through figures. In addition, the persistence properties of the solutions to the Popowicz system in weighted Lp spaces is considered via a large class of moderate weights.
Keywords: Camassa–Holm and Degasperis–Procesi equations; distribution theory; peakon–solutions; persistence property Camassa–Holm and Degasperis–Procesi equations; distribution theory; peakon–solutions; persistence property

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MDPI and ACS Style

Li, Y.; Qin, C. Peakons and Persistence Properties of Solution for the Interacting System of Popowicz. Mathematics 2023, 11, 3529. https://doi.org/10.3390/math11163529

AMA Style

Li Y, Qin C. Peakons and Persistence Properties of Solution for the Interacting System of Popowicz. Mathematics. 2023; 11(16):3529. https://doi.org/10.3390/math11163529

Chicago/Turabian Style

Li, Yaohong, and Chunyan Qin. 2023. "Peakons and Persistence Properties of Solution for the Interacting System of Popowicz" Mathematics 11, no. 16: 3529. https://doi.org/10.3390/math11163529

APA Style

Li, Y., & Qin, C. (2023). Peakons and Persistence Properties of Solution for the Interacting System of Popowicz. Mathematics, 11(16), 3529. https://doi.org/10.3390/math11163529

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