By Jesús Cuevas-Maraver, Panayotis Kevrekidis, Floyd Williams
The sine-Gordon version is a ubiquitous version of Mathematical Physics with a variety of functions extending from coupled torsion pendula and Josephson junction arrays to gravitational and high-energy physics types. the aim of this publication is to give a precis of contemporary advancements during this box, incorporating either introductory history fabric, but in addition with a robust view in the direction of sleek purposes, fresh 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 a variety of researchers during this box, yet serves as an introductory textual content for younger researchers and scholars attracted to the subject. The ebook involves well-selected thematic chapters on diversified mathematical and actual elements of the equation rigorously selected and assigned.
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This booklet fills the necessity for a coherent paintings combining conscientiously reviewed articles right into a accomplished evaluate obtainable to investigate teams and academics. subsequent to basic physics, contributions on topical clinical and fabric technology matters are integrated.
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Phys. G. A. V. Chetkin, Usp. Fiz. Nauk 146, 417 (1985) [Sov. Phys. Uspekhi 28, 564 (1985)] 49. J. A. Maugin, Physica D 14, 88 (1984) 50. M. N. E. Kalugin, Zhurn. Eksp. Teor. Fiz. 75, 2210 (1978) [Sov. Phys. JETP 48, 1113 (1978)] 51. A. M. W. Anderson, Solid State Commun. 14, 703 (1974) 52. J. R. A. E. Trullinger, Phys. Rev. Lett. 36, 432 (1976) 53. C. Scott, Am. J. Phys. 37, 52 (1969) 54. M. Salerno, Physica D 17, 227 (1985) 55. Y. Ishimori, T. Munakata, J. Phys. Soc. Jpn. 51, 3367 (1982) 56. M.
T/ 2 R; n 2 Z; and where 2 is the central difference operator, is of particular interest in its own right. Here is the coupling between adjacent sites and the subscript indexes the lattice sites. In that light, the DsG has been originally proposed as a model for the dynamics of dislocations in crystal-lattices, under the form of the celebrated Frenkel–Kontorova model ; see also the comprehensive book of  and its discussion of some of the historic origins of the model. The prototypical realization of such a discrete system via an array of coupled torsion pendula was originally proposed in the contributions of ; see also .