1. Korteweg-de Vries hierarchy as an asymptotic limit of the Boussinesq system
- Author
-
S. A. Kordyukova
- Subjects
Asymptotic analysis ,Hierarchy (mathematics) ,Mathematical analysis ,Mathematics::Analysis of PDEs ,Statistical and Nonlinear Physics ,Nonlinear system ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Surface wave ,Soliton ,Limit (mathematics) ,Korteweg–de Vries equation ,Representation (mathematics) ,Nonlinear Sciences::Pattern Formation and Solitons ,Mathematical Physics ,Mathematics ,Mathematical physics - Abstract
For the model of surface waves, we perform an asymptotic analysis with respect to a small parameter e for large times where corrections to the approximation described by the Korteweg-de Vries equation must be taken into account. We reveal the appearance of the Korteweg-de Vries hierarchy, which ensures the construction of an asymptotic representation up to the times t ≈ e−2, where the Korteweg-de Vries approximation becomes inapplicable.
- Published
- 2008
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