Dynamics of transformed nonlinear waves in the (3+1)-dimensional B-type Kadomtsev–Petviashvili equation I: Transitions mechanisms

Zhang, Xue; Wang, Lei; Chen, Wei-Qin; Yao, Xuemin; Wang, Xin; Zhao, Yue

doi:10.1016/j.cnsns.2021.106070

Cited by 12 publications

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“…and the speed along the y axis is Based on the analysis of the transformation mechanism of the breathers [33][34][35][36], some conclusions about the one-breather solution (9) of Equation ( 3) can be discussed.…”

Section: One-breather Solution and Transformation Mechanismmentioning

confidence: 99%

“…A breather can be counted as a sort of soliton that propagates periodically along the direction of the intersection with a soliton. Wang et al investigated transformed oneand two-breathers, which are supported by a theoretical framework of a transformation mechanism of nonlinear waves [33][34][35][36]. It was found that there is a relationship of one-way transformation between breathers and nonlinear localized waves by adjusting parameters, including the quasi-anti-dark (kink) soliton, M-shaped (kink) soliton, oscillation M-shaped (kink) soliton, multi-peak (kink) soliton, and quasi-periodic wave.…”

Section: Introductionmentioning

confidence: 98%

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Breathers, Transformation Mechanisms and Their Molecular State of a (3+1)-Dimensional Generalized Yu–Toda–Sasa–Fukuyama Equation

et al. 2023

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A (3+1)-dimensional generalized Yu–Toda–Sasa–Fukuyama equation is considered systematically. N-soliton solutions are obtained using Hirota’s bilinear method. The employment of the complex conjugate condition of parameters of N-soliton solutions leads to the construction of breather solutions. Then, the lump solution is obtained with the aid of the long-wave limit method. Based on the transformation mechanism of nonlinear waves, a series of nonlinear localized waves can be transformed from breathers, which include the quasi-kink soliton, M-shaped kink soliton, oscillation M-shaped kink soliton, multi-peak kink soliton, and quasi-periodic wave by analyzing the characteristic lines. Furthermore, the molecular state of the transformed two-breather is studied using velocity resonance, which is divided into three aspects, namely the modes of non-, semi-, and full transformation. The analytical method discussed in this paper can be further applied to the investigation of other complex high-dimensional nonlinear integrable systems.

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Section: One-breather Solution and Transformation Mechanismmentioning

confidence: 99%