一类(1+1)维变系数复方程的可积性研究  

The Integrability to a(1+1)Dimensional Variable Coefficient Complex Equation

作　　者：张金玉[1] 王丹[1] 耿勇 杨苗苗 王晓丽[1] Zhang Jinyu;Wang Dan;Yong Yang;Geng Miaomiao;Wang Xiaoli(School of Mathematics and Statistics,Qilu University of Technology(Shandong Academy of Sciences),Jinan250353)

机构地区：[1]齐鲁工业大学(山东省科学院)数学与统计学院,济南250353

出　　处：《数学物理学报（A辑）》2023年第4期994-1002,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(12275017);山东省自然科学基金(ZR2019PA020,ZR2020MA049);齐鲁工业大学(山东省科学院)(2022PX092)。

摘　　要：该文基于双Bell多项式与Hirota双线性算子之间的关系,研究了一类(1+1)维变系数复方程的可积性.首先通过适当的变换,构造出方程的双线性表达式、双线性Backlund变换,又通过Hopf-Cole变换得到方程的Lax对,从而证明该方程具有Lax可积性.In this paper,we study the integrability of a(1+1)-dimensional variable coeficient complex equation based on the relationship between multi-dimensional binary bell polynomial and Hirota bilinear operator.Firstly,the bilinear form and bilinear Backlund transformation of the equation are constructed by appropriate transformation.Then the lax pair is obtained by Hopf-Cole transformation,which proves that the equation is Lax integrable.

关 键 词：(1+1)维变系数复方程 BELL多项式 Hirota双线性形式 BACKLUND变换 LAX对 

分 类 号：O175.29[理学—数学]