On the determining equations for the nonclassical reductions of the heat and Burgers' equation

Journal of Mathematical Analysis and Applications

Volumn 270, Issue 2, 2002, Pages 582-589

  Arrigo, D J ^a   Hickling, F ^a  

^a UNIVERSITY OF CENTRAL ARKANSAS   (United States)

Author keywords

Burgers equations; Determining equations; Heat equations; Hopf Cole transformation; Nonclassical symmetry

Indexed keywords

EID: 0037098630     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(02)00091-4     Document Type: Article

References (14)

1. Klassifikation und Integration von gewohnlichen Differentialgleichen zwischen x, y die eine Gruppe von Transformationen gestatten
2. Symmetries and Differential Equations
3. Nonlinear Boundary Value Problems in Science and Engineering
4. The general similarity solution of the heat equation
5. All solutions of standard symmetric linear partial differential equations have classical Lie symmetry
6. Nonclassical symmetry reductions of the linear diffusion equation with a nonlinear source
7. Symmetry reductions and exact solutions of a class of nonlinear heat equation
8. The nonclassical method is more general than the direct method for symmetry reductions: An example of the Fitzhugh-Nagumo equation
9. Nonclassical symmetry reduction: Example of the Boussinesq equation
10. Nonclassical group analysis of the heat equation
11. Nonclassical symmetries are non-existent for the heat equation and rare for nonlinear diffusion
12. Continuous and discrete Burgers' hierarchies
13. Nonclassical symmetries solutions and the methods of Bluman-Cole and Clarkson-Kruskal