Deformed two-dimensional rogue waves in the (2+1)-dimensional Korteweg–de Vries equation  

作　　者：Yulei Cao Peng-Yan Hu Yi Cheng Jingsong He 曹玉雷;胡鹏彦;程艺;贺劲松(Institute for Advanced Study,Shenzhen University,Shenzhen 518060,China;College of Mathematics and Statistics,Shenzhen University,Shenzhen 518060,China;School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]Institute for Advanced Study,Shenzhen University,Shenzhen 518060,China [2]College of Mathematics and Statistics,Shenzhen University,Shenzhen 518060,China [3]School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China

出　　处：《Chinese Physics B》2021年第3期205-214,共10页中国物理B（英文版）

基　　金：Project supported by the National Natural Scinece Foundation of China(Grant Nos.11671219,11871446,12071304,and 12071451).

摘　　要：Within the(2+1)-dimensional Korteweg–de Vries equation framework,new bilinear B¨acklund transformation and Lax pair are presented based on the binary Bell polynomials and gauge transformation.By introducing an arbitrary functionφ(y),a family of deformed soliton and deformed breather solutions are presented with the improved Hirota’s bilinear method.By 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 the obtained solitons.Additionally,twodimensional(2D)rogue waves(localized in both space and time)on the soliton plane are presented,we refer to them 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 functionφ(y).This new idea is also applicable to other nonlinear systems.

关 键 词：two-dimensional(2D)Korteweg-de Vries(KdV)equation Bilinear method Backlund transformation Lax pair deformed 2D rogue wave 

分 类 号：O411.1[理学—理论物理]