-
首先给出非自治Kadomtsev-Petviashvili方程转换为Kadomtsev- Petviashvili方程的一个自相似变换, 然后基于Kadomtsev-Petviashvili方程的Lump解构造了非自治Kadomtsev-Petviashvili方程的有理函数表示的二维单、双、三怪波解, 最后通过合适选取变参数, 用图示说明了它们的演化特征, 并利用快速傅里叶变换算法数值模拟测试了二维单怪波的动力学稳定性. 本文方法对寻找(2 + 1)维非线性波动模型的怪波激发提供了启迪.
-
关键词:
- 二维怪波/
- Kadomtsev-Petviashvili方程/
- 非自治非线性波动模型/
- 自相似变换
Rogue wave is a kind of natural phenomenon that is fascinating, rare, and extreme. It has become a frontier of academic research. The rogue wave is considered as a spatiotemporal local rational function solution of nonlinear wave model. There are still very few (2 + 1)-dimensional nonlinear wave models which have rogue wave solutions, in comparison with soliton and Lump waves that are found in almost all (2 + 1)-dimensional nonlinear wave models and can be solved by different methods, such as inverse scattering method, Hirota bilinear method, Darboux transform method, Riemann-Hilbert method, and homoclinic test method. The structure and evolution characteristics of the obtained (2 + 1)-dimensional rogue waves are quite different from the prototypes of the (1 + 1)-dimensional nonlinear Schrödinger equation. Therefore, it is of great value to study two-dimensional rogue waves. In this paper, the non-autonomous Kadomtsev-Petviashvili equation is first converted into the Kadomtsev-Petviashvili equation with the aid of a similar transformation, then two-dimensional rogue wave solutions represented by the rational functions of the non-autonomous Kadomtsev-Petviashvili equation are constructed based on the Lump solution of the first kind of Kadomtsev-Petviashvili equation, and their evolutionary characteristics are illustrated by images through appropriately selecting the variable parameters and the dynamic stability of two-dimensional single rogue waves is numerically simulated by the fast Fourier transform algorithm. The obtained two-dimensional rogue waves, which are localized in both space and time, can be viewed as a two-dimensional analogue to the Peregrine soliton and thus are a natural candidate for describing the rogue wave phenomena. The method presented here provides enlightenment for searching for rogue wave excitation of (2 + 1)-dimensional nonlinear wave models. We show that two-dimensional rogue waves are localized in both space and time which arise from the zero background and then disappear into the zero background again. These rogue-wave solutions to the non-autonomous Kadomtsev-Petviashvili equation generalize the rogue waves of the nonlinear Schrödinger equation into two spatial dimensions, and they could play a role in physically understanding the rogue water waves in the ocean. -
Keywords:
- two-dimensional rogue wave/
- Kadomtsev-Petviashvili equation/
- nonautonomous nonlinear wave model/
- self-similar transformation
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] -
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] -
[1] 饶继光, 陈生安, 吴昭君, 贺劲松.空间位移 $\mathcal{PT}$ 对称非局域非线性薛定谔方程的高阶怪波解. 必威体育下载 , 2023, 72(10): 104204.doi:10.7498/aps.72.20222298[2] 张解放, 俞定国, 金美贞.二维自相似变换理论和线怪波激发. 必威体育下载 , 2022, 71(1): 014205.doi:10.7498/aps.71.20211417 [3] 张解放, 俞定国, 金美贞.(2+1)维Zakharov方程的自相似变换和线怪波簇激发. 必威体育下载 , 2022, 71(8): 084204.doi:10.7498/aps.71.20211181 [4] 李敏, 王博婷, 许韬, 水涓涓.四阶色散非线性薛定谔方程的明暗孤立波和怪波的形成机制. 必威体育下载 , 2020, 69(1): 010502.doi:10.7498/aps.69.20191384 [5] 张解放, 金美贞.Fokas系统的怪波激发. 必威体育下载 , 2020, 69(21): 214203.doi:10.7498/aps.69.20200710 [6] 焦小玉, 贾曼, 安红利.一类扰动Kadomtsev-Petviashvili方程的雅可比椭圆函数解的收敛性探讨. 必威体育下载 , 2019, 68(14): 140201.doi:10.7498/aps.68.20190333 [7] 王思佳, 顾澄琳, 刘博文, 宋有建, 钱程, 胡明列, 柴路, 王清月.利用非线性脉冲预整形实现脉冲快速自相似放大. 必威体育下载 , 2013, 62(14): 140601.doi:10.7498/aps.62.140601 [8] 陆大全, 胡巍.椭圆响应强非局域非线性介质中的二维异步分数傅里叶变换及光束传输特性. 必威体育下载 , 2013, 62(8): 084211.doi:10.7498/aps.62.084211 [9] 仲生仁.尘埃等离子体中非线性波的叠加效应及稳定性问题. 必威体育下载 , 2010, 59(4): 2178-2181.doi:10.7498/aps.59.2178 [10] 邓一鑫, 涂成厚, 吕福云.非线性偏振旋转锁模自相似脉冲光纤激光器的研究. 必威体育下载 , 2009, 58(5): 3173-3178.doi:10.7498/aps.58.3173 [11] 孟立民, 滕爱萍, 李英骏, 程涛, 张杰.基于自相似模型的二维X射线激光等离子体流体力学. 必威体育下载 , 2009, 58(8): 5436-5442.doi:10.7498/aps.58.5436 [12] 廖龙光, 付虹, 傅秀军.十二次对称准周期结构的自相似变换及准晶胞构造. 必威体育下载 , 2009, 58(10): 7088-7093.doi:10.7498/aps.58.7088 [13] 冯 杰, 徐文成, 刘伟慈, 李书贤, 刘颂豪.高阶色散效应常系数Ginzburg-Landau方程自相似脉冲演化的解析分析. 必威体育下载 , 2008, 57(8): 4978-4983.doi:10.7498/aps.57.4978 [14] 赖小明, 卞保民, 杨 玲, 杨 娟, 卞 牛, 李振华, 贺安之.非奇异宇宙的理想气体自相似模型. 必威体育下载 , 2008, 57(12): 7955-7962.doi:10.7498/aps.57.7955 [15] 冯 杰, 徐文成, 李书贤, 陈伟成, 宋 方, 申民常, 刘颂豪.色散渐减光纤中Ginzburg-Landau方程的自相似脉冲演化的解析解. 必威体育下载 , 2007, 56(10): 5835-5842.doi:10.7498/aps.56.5835 [16] 来娴静, 张解放.两类2+1维非线性波动方程的线性叠加解. 必威体育下载 , 2004, 53(12): 4065-4069.doi:10.7498/aps.53.4065 [17] 董全林, 刘彬.在伽利略坐标变换下的二端面弹性转轴相似动力学方程. 必威体育下载 , 2002, 51(10): 2191-2196.doi:10.7498/aps.51.2191 [18] 闫振亚, 张鸿庆.具有阻尼项的非线性波动方程的相似约化. 必威体育下载 , 2000, 49(11): 2113-2117.doi:10.7498/aps.49.2113 [19] 范恩贵, 张鸿庆.非线性波动方程的孤波解. 必威体育下载 , 1997, 46(7): 1254-1258.doi:10.7498/aps.46.1254 [20] 张珉, 陶瑞宝, 周世勋.具有自相似结构的非均匀复合媒质质量分布的标度指数. 必威体育下载 , 1988, 37(12): 1987-1992.doi:10.7498/aps.37.1987
下载:
计量
- 文章访问数:5596
- PDF下载量:104
- 被引次数:0