(2+1)维Ito方程的孤子解和有理解
PDF下载 (259)肖晶晶,李 彪.(2+1)维Ito方程的孤子解和有理解[J].宁波大学学报(理工版),2019,32(4):63-67.DOI:
XIAO Jingjing,LI Biao.Soliton and rational solutions of the (2+1)-dimensional Ito equation[J].Journal of Ningbo University(Natural Science & Engineering Edition),2019,32(4):63-67.DOI:
| Title: | Soliton and rational solutions of the (2+1)-dimensional Ito equation |
| 作者: | 肖晶晶, 李 彪 |
| Author(s): | XIAO Jingjing, LI Biao |
| 关键词: | Ito方程; Hirota双线性; 孤子解; 长波极限; 呼吸子解; 有理解 |
| Keywords: | Ito equation; Hirota bilinear method; soliton solution; long-wave limit; breather solution; rational solution |
| 分类号: | O175 |
| 文献标识码: | A |
| 摘要: | 基于Hirota双线性方法, 得到(2+1)维Ito方程的双线性形式, 由此可以求得(2+1)维Ito方程的N-孤子解. 在二孤子解的基础上, 对参数取共轭, 可以得到一阶的呼吸子解; 再对二孤子解用长波极限和参数限制, 则可以得到Ito方程的一阶有理解. |
| Abstract: | By employing the Hirota bilinear method, the bilinear form of the (2+1)-dimensional Ito equation can be derived. Based on the bilinear form, N-soliton solutions are constructed. On the condition of parameter conjugations, we can obtain breather solutions to the (2+1)-dimensional Ito equation from the two-soliton solution. By taking a long wave limit and making further parameter constraints, one-order rational solution to the (2+1)-dimensional Ito equation can be derived. |
| 参考文献 /References: | [1] Wang L, Zhang J H, Liu C, et al. Breather transition dynamics, Peregrine combs/walls and modulation instability in a variable-coefficient nonlinear Schr?dinger equation with higher-order effects[EB/OL]. [2018-10-10]. https://arxiv.org/pdf/1603.01456.pdf. [2] Wang L, Li M, Qi F H, et al. Modulational instability, nonautonomous breathers and rouge waves for a variable-coefficient derivative nonlinear Schr?dinger equation in the inhomogeneous[J]. Plasmas, 2015, 22:1-10. [3] Mihalache D. Multidimensional localized structures in optical and Bose-Einstein condensates: A selection of recent studies[J]. Romanian Journal of Physics, 2014, 59:295-312. [4] Malomed B, Torner L, Wise F, et al. On multidimensional solitons and their legacy in contemporary atomic, molecular and optical physics[J]. Journal of Physics B-Atomic Molecular and Optical Physics, 2016, 49(17):1-32. [5] Bagnato V S, Frantzeskakis D J, Kevrekidis P G, et al. Bose-Einstein condensation: Twenty year after[J]. Romanian Journal of Physics, 2015, 67:251-253. [6] Matveev V B, Salle M A. Darboux transformation and solitons[EB/OL]. [2018-10-10]. https://zbmath.org/0744.35045. [7] 谷超豪, 胡和生, 周子翔. 孤子理论中的达布变换及其几何应用[M]. 上海: 上海科学技术出版社, 1999:1-47. [8] Matsuno Y. Bilinear transformation method[EB/OL]. [2018-10-10]. https://zbmath.org/0552.35001. [9] Hirota R. The Direct Method in Soliton Theory[M]. Cambridge: Cambridge University Press, 2004:1-58. [10] Ablowitz M J. Solitons, Nonlinear Evolution Equations and Inverse Scattering[M]. Cambridge: Cambridge University Press, 1992:70-152. [11] Dickey L A. Solitons Equations and Hamiltonian Systems[M]. Singapore: World Scientific, 1991:7-20. [12] Vladimirov A, Maczka C. Exact solutions of generalized burgers equation, describing travelling fronts and their interaction[J]. Reports on Mathematical Physics, 2007, 60(2):317-328. [13] Bluman G W, Kumei S. Symmetries and differential equations[EB/OL]. [2018-10-10]. https://link.springer.com/book/10.1007%2F978-1-4757-4307-4. [14] Ohta Y, Wang D S, Yang J. General N-dark-dark solitons in the coupled nonlinear Schr?dinger equations[J]. Studies in Applied Mathematics, 2011, 17(4):345-371. [15] Rao J G, Cheng Y, He J S. Rational and semi-rational solution of the nonlocal Davey-Stewardton[J]. Studies in Applied Mathematics, 2017, 139:568-598. [16] Wang X B, Tian S F, Qin C Y, et al. Dynamics of the breathers, rogue waves and solitary waves in the (2+1)-dimensional Ito equation[J]. Applied Mathematics Letters, 2018, 68:40-47. [17] Yang J Y, Ma W X, Qin Z Y. Lump and lump-soliton solutions to the (2+1)-dimensional Ito equation[J]. Analysis and Mathematical Physics, 2018, 8:427-436. [18] Zhang Y, Chen D Y. N-soliton-like solution of Ito equation[J]. Communications in Theoretical Physics, 2004, 42:641-644. |
| 备注/Memo: | 收稿日期: 2019－01－20. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/基金项目: 国家自然科学基金（11775121）. 第一作者: 肖晶晶（1992－）, 女, 河南开封人, 在读硕士研究生, 主要研究方向: 非线性偏微分方程. E-mail: 1348130105@qq.com*通信作者: 李彪（1971－）, 男, 湖南会同人, 博士/教授, 主要研究方向: 非线性数学物理与数学机械化. E-mail: libiao@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
