Decay of solutions of dispersive equations and Poisson brackets in algebraic geometry
In the first part of this work we will study the spatial decay of solutions of nonlinear dispersive equations. The starting point will be the Korteweg-de Vries (KdV) equation, for which it will be proved that a decay of exponential type is degraded in time, and that the exhibited decay is optimal. I...
- Autores:
-
León Gil, Carlos Augusto
- Tipo de recurso:
- Fecha de publicación:
- 2017
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/58837
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/58837
http://bdigital.unal.edu.co/55821/
- Palabra clave:
- 51 Matemáticas / Mathematics
KdV equation
Evolution dispersive equations
Decay properties
Poisson structures
Liouville integrable systems
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | In the first part of this work we will study the spatial decay of solutions of nonlinear dispersive equations. The starting point will be the Korteweg-de Vries (KdV) equation, for which it will be proved that a decay of exponential type is degraded in time, and that the exhibited decay is optimal. In the second part we will make an exposition on Symplectic and Poisson Geometry with connections in Classical Mechanics to motivate a more abstract view of Poisson structures. With these preliminaries we can then give way to a little digression on Integrable Systems, and discuss the notion of complete integratbility in the sense of Liouville |
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