By Jesús Cuevas-Maraver, Panayotis Kevrekidis, Floyd Williams

ISBN-10: 3319067214

ISBN-13: 9783319067216

ISBN-10: 3319067222

ISBN-13: 9783319067223

The sine-Gordon version is a ubiquitous version of Mathematical Physics with quite a lot of functions extending from coupled torsion pendula and Josephson junction arrays to gravitational and high-energy physics types. the aim of this ebook is to offer a precis of modern advancements during this box, incorporating either introductory heritage fabric, but in addition with a robust view in the direction of glossy functions, contemporary experiments, advancements in regards to the life, balance, dynamics and asymptotics of nonlinear waves that come up within the version. This publication is of specific curiosity to quite a lot of researchers during this box, yet serves as an introductory textual content for younger researchers and scholars drawn to the subject. The booklet includes well-selected thematic chapters on assorted mathematical and actual elements of the equation conscientiously selected and assigned.

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Fistul, Y. V. Ustinov, Nature 425, 155 (2003) 36. V. S. V. Shmidt, J. Low Temp. Phys. 45, 497 (1981) 37. F. Volkov, Pis’ma Zhurn. Eksp. Teor. Fiz. 45, 299 (1987) [JETP Lett. 45, 376 (1987)] 38. S. A. Malomed, Phys. Rev. B 37, 9325 (1988) 39. V. Ustinov, H. Kohlstedt, M. F. Pedersen, G. Hallimanns, G. Heident, Phys. Rev. B 48, 10614 (1993) 40. S. V. Ustinov, H. Kohlstedt, A. F. Pedersen, Phys. Rev. B 50, 12905 (1994) The sine-Gordon Model: General Background. . 41. 42. 43. 44. 45. 46. 47. 48. 29 S.

Chong, J. G. Kevrekidis Abstract In the present chapter, we consider two prototypical Klein–Gordon models: the integrable sine-Gordon equation and the non-integrable 4 model. We focus, in particular, on two of their principal solutions, namely the kinklike 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.

Note that expression (53), although it may seem divergent, actually vanishes at jzj ! 1. In the case of the double sG equation (7), the perturbation term, sin . =2/, prevents the existence of 2 kinks, such as those given by Eq. (23), but it gives rise to stable bound states of two 2 kinks in the form of a 4 kink. It may be found in an exact form, in spite of the nonintegrability of the double sG equation. A. Malomed This bound state may exist in an excited state, with the two constituent 2 kinks featuring relative oscillations of their positions with p frequency which was predicted by means of the perturbation theory too, !

### The sine-Gordon Model and its Applications: From Pendula and Josephson Junctions to Gravity and High-Energy Physics by Jesús Cuevas-Maraver, Panayotis Kevrekidis, Floyd Williams

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