Volume 125, Number 1, January 2019
|Number of page(s)||6|
|Section||Physics of Gases, Plasmas and Electric Discharges|
|Published online||21 January 2019|
Auto-Bäcklund transform and exact solutions to local conformable time-fractional viscous Burgers system
School of Mathematics and Statistics, Anhui Normal University - Wuhu 241002, China
Received: 7 October 2018
Accepted: 20 December 2018
The classical Burgers equation is one of important nonlinear models in fluid mechanics, which is often used to describe acoustical waves, electromagnetic waves, etc. This paper generalizes the discussions on the classical Burgers equation to that for the multi-dimensional local conformable time-fractional Burgers system. The corresponding auto-Bäcklund and Hopf-Cole transforms are also obtained. By solving the local fractional linear heat equation, we derive many exact solutions and, to the best of our knowledge, some of them are very new. The impact of the fractional derivative on the solutions is also discussed.
PACS: 52.35.Mw – Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.) / 05.45.Yv – Solitons
© EPLA, 2019
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.