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Planar, solitary, and spiral waves of the Burgers-CGL equations for flames governed by a sequential reaction.
- Source :
-
Journal of Mathematical Physics . 2017, Vol. 58 Issue 10, p1-19. 19p. 7 Graphs. - Publication Year :
- 2017
-
Abstract
- This paper studied the planar, solitary, and spiral waves of the coupled Burgerscomplex Ginzburg-Landau (Burgers-CGL) equations, which were derived from the nonlinear evolution of the coupled long-scale oscillatory and monotonic instabilities of a uniformly propagating combustion wave governed by a sequential chemical reaction having two flame fronts corresponding to two reaction zones with a finite separation distance between them. First, some exact solutions including the planar and solitary waves for the one-dimensional Burgers-CGL equations that are obtained by subtle transforms and the hyperbolic tangent function expansion method. Second, some spiral waves for the two-dimensional Burgers-CGL equations are investigated. The existence of the spiral waves is proved rigorously by Schauder's fixed point theorem applied to a class of functions, and the approximate solutions are also obtained by the power series expansion method. Furthermore, some numerical simulations are carried out near 0 < r < 1, since the core of the spiral wave is a singular point in the view of mathematics, and the results verify the theoretical analysis. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 58
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 126024750
- Full Text :
- https://doi.org/10.1063/1.5008328