TY - JOUR
T1 - Painlevé Analysis and Auto-Bäcklund Transformation for a General Variable Coefficient Burgers Equation with Linear Damping Term
AU - Shang , Yadong
AU - Zheng , Xiaoru
JO - Journal of Nonlinear Modeling and Analysis
VL - 1
SP - 133
EP - 141
PY - 2024
DA - 2024/03
SN - 6
DO - http://doi.org/10.12150/jnma.2024.133
UR - https://global-sci.org/intro/article_detail/jnma/22970.html
KW - Painlevé property, auto-Bäcklund transformation, a gVC Burgers
equation with linear damping term, exact solutions.
AB - <p style="text-align: justify;">This paper investigates a general variable coefficient (gVC) Burgers equation with linear damping term. We derive the Painlevé property of the
equation under certain constraint condition of the coefficients. Then we obtain an auto-Bäcklund transformation of this equation in terms of the Painlevé property. Finally, we find a large number of new explicit exact solutions of
the equation. Especially, infinite explicit exact singular wave solutions are obtained for the first time. It is worth noting that these singular wave solutions
will blow up on some lines or curves in the $(x,t)$ plane. These facts reflect
the complexity of the structure of the solution of the gVC Burgers equation
with linear damping term. It also reflects the complexity of nonlinear wave
propagation in fluid from one aspect.</p>