Critical velocity in kink solutions of the sine-Gordon equation
The goal of this work is to present a way to deduce the value of the critical velocity observed in soliton-like solutions of a perturbed version of the sine-Gordon equation. To do so, an ODE system is obtained from the perturbed sine-Gordon equation using a variational approach; the resulting Hamilt...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/106773 |
| Acceso en línea: | https://hdl.handle.net/2117/106773 |
| Access Level: | acceso abierto |
| Palabra clave: | Differentiable dynamical systems Sine-Gordon Kink Critical Velocity Melnikov Invariant Manifolds Periodic Variational Perturbation Sistemes dinàmics diferenciables Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics |
| Sumario: | The goal of this work is to present a way to deduce the value of the critical velocity observed in soliton-like solutions of a perturbed version of the sine-Gordon equation. To do so, an ODE system is obtained from the perturbed sine-Gordon equation using a variational approach; the resulting Hamiltonian system is then studied. From that, a Melnikov integral formula for the critical velocity is deduced via an energy balance reasoning. Finally, the problem is approached from a geometrical point of view that allows for an interpretation of the previous results in terms of intersections of invariant manifolds of periodic orbits. |
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