On Burgers equation on a time-space scale

Advances in Difference Equations

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