Sine-Gordon Equation: From Discrete to Continuum
In the present Chapter, we consider two prototypical Klein-Gordon models: the integrable sine- Gordon equation and the non-integrable φ4 model. We focus, in particular, on two of their prototypical solutions, namely the kink-like heteroclinic connections and the time-periodic, exponentially localize...
| Autores: | , , , |
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| Tipo de recurso: | capítulo de libro |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/83341 |
| Acceso en línea: | https://hdl.handle.net/11441/83341 https://doi.org/10.1007/978-3-319-06722-3__2 |
| Access Level: | acceso abierto |
| Palabra clave: | ϕ4 model Anti-continuum limit Breathers Continuum and discrete models Kinks Klein–Gordon lattices Klein–Gordon PDEs Nanopteron PT-symmetry |
| Sumario: | In the present Chapter, we consider two prototypical Klein-Gordon models: the integrable sine- Gordon equation and the non-integrable φ4 model. We focus, in particular, on two of their prototypical solutions, namely the kink-like heteroclinic connections and the time-periodic, exponentially localized in space breather waveforms. Two limits of the discrete variants of these models are contrasted: on the one side, the analytically tractable original continuum limit, and on the opposite end, the highly discrete, so-called anti-continuum limit of vanishing coupling. Numerical computations are used to bridge these two limits, as regards the existence, stability and dynamical properties of the waves. Finally, a recent variant of this theme is presented in the form of PT -symmetric Klein-Gordon field theories and a number of relevant results are touched upon. |
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