(2 + 1)维Hirota-Satsuma-Ito方程的呼吸波与不同非线性波之间的态转换
State Transformations between the Breather Wave and Different Nonlinear Waves for the (2 + 1)-Dimensional Hirota-Satsuma-Ito Equation
摘要: 本文基于Hirota双线性方法，研究了(2 + 1)维Hirota-Satsuma-Ito方程。在特定情况下，呼吸波可以转化为其他类型的非线性波，包括W型、M型、振荡W型、振荡M型和准周期型波，并分析了这些非线性波的动力学特性。基于特征线分析，得到了呼吸波与其他非线性波之间的转换条件。研究结果丰富了(2 + 1)维非线性波的动力学特性。
Abstract: In this paper, the (2 + 1)-dimensional Hirota-Satsuma-Ito equation is studied based on the Hirota bilinear method. Under certain circumstances, the breather wave can be transformed into other types of nonlinear waves, including W-type, M-type, oscillating-W-type, oscillating-M-type and quasi-periodic-type waves, and the dynamic characteristics of these nonlinear waves are analyzed. Based on the characteristic line analysis, the conversion condition between the breather wave and other nonlinear waves is obtained. The results enrich the dynamic characteristics of the (2 + 1)-dimensional nonlinear waves.
文章引用：张丹丹. (2 + 1)维Hirota-Satsuma-Ito方程的呼吸波与不同非线性波之间的态转换[J]. 应用数学进展, 2021, 10(4): 1403-1409. https://doi.org/10.12677/AAM.2021.104149

参考文献

[1] Solli, D.R., Ropers, C., Koonath, P. and Jalali, B. (2007) Optical Rogue Waves. Nature, 450, 1054-1057. [Google Scholar] [CrossRef] [PubMed]
[2] Bludov, Y.V., Konotop, V.V. and Akhmediev, N. (2009) Matter Rogue Waves. Physical Review A, 80, Article ID: 033610. [Google Scholar] [CrossRef] 
[3] Chabchoub, A., Hoffmann, N.P. and Akhmediev, N. (2011) Rogue Wave Observation in a Water Wave Tank. Physical Review Letters, 106, Article ID: 204502. [Google Scholar] [CrossRef] 
[4] Kibler, B., Fatome, J., Finot, C., Millot, G., Dias, F., Genty, G., Akhmediev, N. and Dudley, J.M. (2010) The Peregrine Soliton in Nonlinear Fibre Optics. Nature Physics, 6, 790-795. [Google Scholar] [CrossRef] 
[5] Bailung, H., Sharma, S.K. and Nakamura, Y. (2011) Observation of Peregrine Solitons in a Multi-Component Plasma with Negative Ions. Physical Review Letters, 107, Article ID: 255005. [Google Scholar] [CrossRef] 
[6] Dai, C.Q., Wang, Y.Y. and Zhang, J.F. (2020) Managements of Scalar and Vector Rogue Waves in a Partially Nonlocal Nonlinear Medium with Linear and Harmonic Potentials. Nonlinear Dynamics, 102, 379-391. [Google Scholar] [CrossRef] 
[7] Akhmediev, N., Soto-Crespo, J.M. and Ankiewicz, A. (2009) Extreme Waves That Appear from Nowhere: On the Nature of Rogue Waves. Physics Letters A, 373, 2137-2145. [Google Scholar] [CrossRef] 
[8] Agrawal, G.P. (2006) Nonlinear Fiber Optics. 4th Edition, Academic Press, San Diego. [Google Scholar] [CrossRef] 
[9] Ma, W.X. (2015) Lump Solutions to the Kadomtsev-Petviashvili Equation. Physics Letters A, 379, 1975-1978. [Google Scholar] [CrossRef] 
[10] Singh, N. and Stepanyants, Y. (2016) Obliquely Propagating Skew KP Lumps. Wave Motion, 64, 92-102. [Google Scholar] [CrossRef] 
[11] Zhou, Y., Manukure, S. and Ma, W.X. (2019) Lump and Lump-Soliton Solutions to the Hirota-Satsuma-Ito Equation. Communications in Nonlinear Science and Numerical Simulation, 68, 56-62. [Google Scholar] [CrossRef] 
[12] Zhou, Y. and Manukure, S. (2019) Complexiton Solutions to the Hirota-Satsuma-Ito Equation. Mathematical Methods in the Applied Sciences, 42, 2344-2351. [Google Scholar] [CrossRef] 
[13] Liu, Y.Q., Wen, X.Y. and Wang, D.S. (2019) The N-Soliton Solution and Localized Wave Interaction Solutions of the (2+1)-Dimensional Generalized Hirota-Satsuma-Ito Equation. Computers & Mathematics with Applications, 77, 947-966. [Google Scholar] [CrossRef] 
[14] Liu, J.G., Zhu, W.H. and Li, Z. (2020) Multi-Wave, Breather Wave, and Interaction Solutions of the Hirota-Satsuma-Ito Equation. European Physical Journal plus, 135, 20. [Google Scholar] [CrossRef] 
[15] Hirota, R. (2004) The Direct Method in Soliton Theory. Cambridge University Press, Cambridge. [Google Scholar] [CrossRef] 

为你推荐