两个广义短脉冲方程的Bäcklund变换及其应用  

On two Generalized Short Pulse Equations:Backlund Transformations and Applications

作　　者：毛辉 MAO Hui(School of Mathematics and Statistics,Nanning Normal University,Nanning 530001,China)

机构地区：[1]南宁师范大学数学与统计学院,南宁530001

出　　处：《应用数学学报》2021年第3期340-354,共15页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11905110,11871471);广西自然科学基金(2018GXNSFBA050020);广西高校中青年教师科研基础能力提升项目(2019KY0417)资助.

摘　　要：本文研究了两个广义短脉冲方程的Backlund变换.利用互反变换和连带广义短脉冲方程,构造了这两个广义短脉冲方程的即涉及因变量又涉及自变量的Backlund变换.基于Bäcklund变换,导出了相应的非线性叠加公式,并给出了广义短脉冲方程的一些精确解.In this paper,Backlund transformations for two generalized short pulse equations are considered.With the help of reciprocal transformation and the associated generalized short pulse equations,the Backlund transformations,which involves both independent and dependent variables,are constructed for the generalized short pulse equations.Based on the Backlund transformations,the corresponding nonlinear superposition formulas are also worked out and some solutions to the generalized short pulse equations are presented.

关 键 词：广义短脉冲方程 BACKLUND变换 非线性叠加公式 cuspon解 

分 类 号：O175.24[理学—数学]