期刊论文详细信息
Advances in Difference Equations
On Burgers equation on a time-space scale
Logan Bonecutter1  Anita Mizer1  Gro Hovhannisyan1 
[1] Kent State University at Stark, North Canton, USA
关键词: Burgers equation;    heat equation;    partial differential equations;    time scales;    spectral expansion;    Fourier series;    soliton-like nonlinear equations;    Lax equation;    35Q51;    35K05;    34N05;   
DOI  :  10.1186/s13662-015-0622-4
学科分类:数学(综合)
来源: SpringerOpen
PDF
【 摘 要 】

The Lax equation is introduced on a time-space scale. The viscous Burgers and the nonlinear Schrodinger dynamic equations on a time-space scale are deduced from the Lax equation by using the Ablowitz-Kaup-Newel-Segur-Ladik method. It is shown that the Burgers equation turns to the heat equation on a time-space scale by the Cole-Hopf transformation. Further, using the separation of variables, we deduce the formula for solutions of the boundary value problem for the heat and Burgers equation on a time-space scale in terms of Fourier series by Hilger exponential functions.

【 授权许可】

CC BY   

【 预 览 】
附件列表
Files Size Format View
RO201904021444695ZK.pdf 1578KB PDF download
  文献评价指标  
  下载次数:12次 浏览次数:6次