一类微分-差分方程的孤子解

吉林大学学报(理学版) ›› 2019, Vol. 57 ›› Issue (04): 762-765.

一类微分-差分方程的孤子解

樊方成，周冉

吉林大学数学学院, 长春 130012

收稿日期:2019-01-15 出版日期:2019-07-26 发布日期:2019-07-11
通讯作者: 樊方成 E-mail:fanfc16@mails.jlu.edu.cn

Soliton Solutions of a Class of DifferentialDifference Equations

FAN Fangcheng, ZHOU Ran

College of Mathematics, Jilin University, Changchun 130012, China

Received:2019-01-15 Online:2019-07-26 Published:2019-07-11
Contact: FAN Fangcheng E-mail:fanfc16@mails.jlu.edu.cn

摘要/Abstract

摘要： 先根据一类微分差分方程的Lax对, 构建该方程的N-fold Darboux变换, 然后应用Darboux变换, 得到该方程的精确解, 通过软件画图给出该方程的1-孤子解、 2-孤子解、 3-孤子解和4-孤子解, 并讨论3-孤子解和4-孤子解的弹性作用: 相互作用后, 孤子形状和振幅不发生变化.

关键词: 微分-差分方程, N-fold Darboux变换, 孤子解

Abstract: Firstly, based on Lax pairs of a class of differentialdifference equations, the N-fold Darboux transformation was constructed, and then we obtained the exact solutions of the equation by using the Darboux transformation.
Through software drawing, we gave the one, two, three and foursoliton solutions of the equation, and dicussed the
elastic effect among the three solitons and four solitons： solitonic shapes and amplitudes do not change after interaction.

Key words: differentialdifference equation, N-fold Darboux transformation, soliton solution

中图分类号:

O175.29

樊方成, 周冉. 一类微分-差分方程的孤子解[J]. 吉林大学学报(理学版), 2019, 57(04): 762-765.

FAN Fangcheng, ZHOU Ran. Soliton Solutions of a Class of DifferentialDifference Equations[J]. Journal of Jilin University Science Edition, 2019, 57(04): 762-765.

[1]	樊方成, 周冉. 一类离散可积系统的孤子解[J]. 吉林大学学报(理学版), 2020, 58(6): 1303-1308.
[2]	黄坤, 吕悦. (2+1)维MKdV方程的Darboux变换及其孤子解[J]. 吉林大学学报(理学版), 2013, 51(04): 573-579.