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 | |
【 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 】
Files | Size | Format | View |
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RO201904021444695ZK.pdf | 1578KB | download |