Back to Search
Start Over
Approximate similarity reduction for singularly perturbed Boussinesq equation via symmetry perturbation and direct method.
- Source :
- Journal of Mathematical Physics; Sep2008, Vol. 49 Issue 9, p093505, 11p
- Publication Year :
- 2008
-
Abstract
- We investigate the singularly perturbed Boussinesq equation in terms of the approximate symmetry perturbation method and the approximate direct method. The similarity reduction solutions and similarity reduction equations of different orders display formal coincidence for both methods. Series reduction solutions are consequently derived. For the approximate symmetry perturbation method, similarity reduction equations of the zero order are equivalent to the Painlevé IV, Painlevé I, and Weierstrass elliptic equations. For the approximate direct method, similarity reduction equations of the zero order are equivalent to the Painlevé IV, Painlevé II, Painlevé I, or Weierstrass elliptic equations. The approximate direct method yields more general approximate similarity reductions than the approximate symmetry perturbation method. [ABSTRACT FROM AUTHOR]
- Subjects :
- APPROXIMATION theory
PERTURBATION theory
MATHEMATICAL symmetry
MATHEMATICS
EQUATIONS
Subjects
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 49
- Issue :
- 9
- Database :
- Complementary Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 34621900
- Full Text :
- https://doi.org/10.1063/1.2976034