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- Title
Painlevé Analysis and Auto-Bäcklund Transformation for a General Variable Coefficient Burgers Equation with Linear Damping Term.
- Authors
Yadong Shang; Xiaoru Zheng
- Abstract
This paper investigates a general variable coefficient (gVC) Burgers equation with linear damping term. We derive the Painlev'e 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 Painlev'e 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.
- Subjects
BURGERS' equation; NONLINEAR wave equations; COEFFICIENTS (Statistics); NONLINEAR partial differential operators; MATHEMATICS
- Publication
Journal of Nonlinear Modeling & Analysis, 2024, Vol 6, Issue 1, p133
- ISSN
2562-2854
- Publication type
Article
- DOI
10.12150/jnma.2024.133