一类(1+1)维变系数复方程的可积性研究

数学物理学报 ›› 2023, Vol. 43 ›› Issue (4): 994-1002.

一类(1+1)维变系数复方程的可积性研究

张金玉(),王丹,耿勇,杨苗苗,王晓丽^*()

齐鲁工业大学(山东省科学院)数学与统计学院济南 250353

收稿日期:2022-08-26 修回日期:2023-04-10 出版日期:2023-08-26 发布日期:2023-07-03
通讯作者: 王晓丽 E-mail:zhangjinyu0611@163.com;wxlspu@qlu.edu.cn
作者简介:张金玉, E-mail: zhangjinyu0611@163.com
基金资助:
国家自然科学基金(12275017);山东省自然科学基金(ZR2019PA020);山东省自然科学基金(ZR2020MA049);齐鲁工业大学(山东省科学院)(2022PX092)

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

Zhang Jinyu(),Wang Dan,Geng Yong,Yang Miaomiao,Wang Xiaoli^*()

School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353

Received:2022-08-26 Revised:2023-04-10 Online:2023-08-26 Published:2023-07-03
Contact: Xiaoli Wang E-mail:zhangjinyu0611@163.com;wxlspu@qlu.edu.cn
Supported by:
NSFC(12275017);NSFSD(ZR2019PA020);NSFSD(ZR2020MA049);QLU(2022PX092)

摘要/Abstract

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Bäcklund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.

关键词: (1+1)维变系数复方程, Bell多项式, Hirota双线性形式, B?cklund变换, Lax对

Abstract:

In this paper, we study the integrability of a (1+1)-dimensional variable coefficient complex equation based on the relationship between multi-dimensional binary bell polynomial and Hirota bilinear operator. Firstly, the bilinear form and bilinear Bäcklund 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.

Key words: (1+1)-dimensional variable coefficient complex equation, Bell polynomials, Hirota bilinear form, B?cklund transformation, Lax pair

中图分类号:

O175.29:文献标识码:A

张金玉,王丹,耿勇,杨苗苗,王晓丽. 一类(1+1)维变系数复方程的可积性研究[J]. 数学物理学报, 2023, 43(4): 994-1002.

Zhang Jinyu,Wang Dan,Geng Yong,Yang Miaomiao,Wang Xiaoli. The Integrability to a (1+1) Dimensional Variable Coefficient Complex Equation[J]. Acta mathematica scientia,Series A, 2023, 43(4): 994-1002.

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