Chapter of Book
Sine-Gordon Equation: From Discrete to Continuum
Author/s | Chirilus-Bruckner, Martina
Chong, Christopher Kevrekidis, Panayotis G. Cuevas-Maraver, Jesús |
Department | Universidad de Sevilla. Departamento de Física Aplicada I |
Publication Date | 2014 |
Deposit Date | 2019-02-21 |
Published in |
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ISBN/ISSN | 978-3-319-06722-3 |
Abstract | 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 ... 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. |
Citation | Chirilus-Bruckner, M., Chong, C.,...,Cuevas-Maraver, J. (2014). Sine-Gordon Equation: From Discrete to Continuum. En The sine-Gordon Model and its Applications (pp. 31-57). Switzerland: Springer International Publishing |
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