论文标题
（2+1） - 维格 - de Vries方程中变形的二维流氓波
Deformed two-dimensional rogue waves in the (2+1)-dimensional Korteweg-de Vries equation
论文作者
论文摘要
在（2 + 1）二维的korteweg-de Vries方程框架中，根据二进制钟形多项式和量规变换，提出了新的双线反向篮板变换和宽松对。通过引入任意函数，用改进的hirotas双线性方法提出了一个变形的孤子和变形的呼吸溶液家族。选择适当的参数，其有趣的动态行为以三维图显示。此外，通过占据获得的孤子的极限，可以产生新颖的理性解决方案。此外，提出了孤子平面上的二维[2D]流氓波（位于空间和时间上），我们将其称为变形的2D流氓波。所获得的变形2D流氓波可以看作是Soliton平面上圆球的2D类似物，并详细分析了其演化过程。变形的2D Rogue Wave解决方案成功地构建了与任意函数密切相关的。这个新想法也适用于其他非线性系统。
Within the (2 + 1)-dimensional Korteweg-de Vries equation framework, new bilinear Backlund transformation and Lax pair are presented based on the binary Bell polynomials and gauge transformation. By introducing an arbitrary function, a family of deformed soliton and deformed breather solutions are presented with the improved Hirotas bilinear method. Choosing the appropriate parameters, their interesting dynamic behaviors are shown in three-dimensional plots. Furthermore, novel rational solutions are generated by taking the limit of obtained solitons. Additionally, two dimensional [2D] rogue waves (localized in both space and time) on the soliton plane are presented, we refer to it as deformed 2D rogue waves. The obtained deformed 2D rogue waves can be viewed as a 2D analog of the Peregrine soliton on soliton plane, and its evolution process is analyzed in detail. The deformed 2D rogue wave solutions are constructed successfully, which are closely related to the arbitrary function. This new idea is also applicable to other nonlinear systems.
