By Jesús Cuevas-Maraver, Panayotis Kevrekidis, Floyd Williams
The sine-Gordon version is a ubiquitous version of Mathematical Physics with a variety of purposes extending from coupled torsion pendula and Josephson junction arrays to gravitational and high-energy physics versions. the aim of this booklet is to offer a precis of contemporary advancements during this box, incorporating either introductory history fabric, but additionally with a robust view in the direction of smooth functions, contemporary experiments, advancements concerning the lifestyles, balance, dynamics and asymptotics of nonlinear waves that come up within the version. This booklet 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 ebook involves well-selected thematic chapters on assorted mathematical and actual points of the equation rigorously selected and assigned.
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Extra info for The sine-Gordon Model and its Applications: From Pendula and Josephson Junctions to Gravity and High-Energy Physics
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The resonance actually takes place between the periodic passage of lattice sites by the moving discrete kink and the periodic action of the ac driving force, which makes it possible to balance the friction force, even though the drive has no dc component. The stability of such ac-driven regimes was confirmed by direct simulations [85]. This regime was experimentally demonstrated for fluxons in a long circular acdriven JJ with a periodic lattice of local defects [86]. ipn i t/. This consideration is most relevant for the circular lattice of integer length L, hence the phonon wavenumbers are selected by relation pL D 2 m, with arbitrary integer m.
15] and references therein. At this continuum limit, one of the particularly intriguing features that were discovered early on was the existence of a fractal structure [14] in the collisions between the fundamental nonlinear waves, once again, a kink and an antikink in this model. Notice here the fundamental contrast of such a fractal structure with the completely inoccuous collisions arising in the sine-Gordon integrable model, whereby the integrability and presence of an infinite number of conservation laws dictates a completely elastic collision outcome (and a mere phase-shifting of the kink or even breather solitons).