Rational solutions of an extended (2+1)-dimensional Camassa-Holm- Kadomtsev-Petviashvili equation in liquid drop

Zhe Ji; Yifan Nie; Lingfei Li; Yingying Xie; Mancang Wang; Zhe Ji; Yifan Nie; Lingfei Li; Yingying Xie; Mancang Wang

doi:10.3934/math.2023162

AIMS Mathematics

2023, Volume 8, Issue 2: 3163-3184. doi: 10.3934/math.2023162

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Research article

Rational solutions of an extended (2+1)-dimensional Camassa-Holm- Kadomtsev-Petviashvili equation in liquid drop

1.
School of Economics and Management, Northwest University, Xi'an 710127, Shaanxi, China
2.
School of Business Administration, Xi'an Eurasia University, Xi'an 710065, Shaanxi, China
3.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, China

Received: 27 July 2022 Revised: 25 October 2022 Accepted: 30 October 2022 Published: 16 November 2022
MSC : 35A08, 35C05, 35C07, 35C08, 35C11

This paper investigates rational solutions of an extended Camassa-Holm-Kadomtsev-Petviashvili equation, which simulates dispersion's role in the development of patterns in a liquid drop, and describes left and right traveling waves like the Boussinesq equation. Through its bilinear form and symbolic computation, we derive some multiple order rational and generalized rational solutions and analyze their dynamic features, such as the connection between rational solution and bilinear equation, scatter behavior, moving path, and exact location of the soliton. The obtained solutions demonstrate two wave forms: multi-lump and multi-wave that consist of three, six and eight lump waves or two, three and four line waves. Moreover, different from the multi-wave solitons, stationary multiple dark waves are presented.
- CH-KP equation,
- rogue wave,
- rational solution,
- symbolic computation
Citation: Zhe Ji, Yifan Nie, Lingfei Li, Yingying Xie, Mancang Wang. Rational solutions of an extended (2+1)-dimensional Camassa-Holm- Kadomtsev-Petviashvili equation in liquid drop[J]. AIMS Mathematics, 2023, 8(2): 3163-3184. doi: 10.3934/math.2023162

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Abstract

This paper investigates rational solutions of an extended Camassa-Holm-Kadomtsev-Petviashvili equation, which simulates dispersion's role in the development of patterns in a liquid drop, and describes left and right traveling waves like the Boussinesq equation. Through its bilinear form and symbolic computation, we derive some multiple order rational and generalized rational solutions and analyze their dynamic features, such as the connection between rational solution and bilinear equation, scatter behavior, moving path, and exact location of the soliton. The obtained solutions demonstrate two wave forms: multi-lump and multi-wave that consist of three, six and eight lump waves or two, three and four line waves. Moreover, different from the multi-wave solitons, stationary multiple dark waves are presented.

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