Resonant soliton-impurity interactions

Abstract

We describe a new type of soliton-impurity interaction and demonstrate that the soliton can be totally reflected by an attractive impurity if its initial velocity lies in certain resonance "windows." This effect has an analogy with the resonance phenomena in kink-antikink collisions [Campbell, Schonfeld, and Wingate, Physica (Amsterdam) 9D, 1 (1983)], and it can be explained by a resonant energy exchange between the soliton and the impurity mode. Taking the sine-Gordon and 0"^ models as examples, we find a number of resonance windows by numerical simulations and develop a collective-coordinate approach to describe the effect analytically.

Interaction of noncommutative solitons with defects

“…The effects of medium disorders and impurities can be added to the equation of motion as perturbative terms [7,8]. These effects also can be taken into account by making some parameters of the equation of motion to be function of space or time [9,10].…”

“…For this situation equations (4) reduce to [6] ∂∂φ 0 = λsinφ 0 ∂∂φ 1 = λφ 1 cosφ 0 (7) and the constraint equation…”

Decay to bound states of a soliton in a well

“…Solitons are now generated in nonlinear transmission lines, optical fibers (bright and dark solitons), Josephson junctions, crystals, etc. [1] Almost a decade ago Kivshar et al [2] noted that a soliton interacting with an impurity modelled as an external potential or a space dependent mass term, generates a wealth of phenomena ranging from repulsion by an attractive impurity and trapping of a positive kinetic energy soliton in an attractive well. The mechanism of trapping consists in a soliton arriving at the site of an attractive potential and oscillating inside it for an infinite time without the possiblity of reemerging from it.…”

“…Trapping can be understood in terms of a few degrees of freedom for the soliton [2], namely, the center of the soliton, a shape mode excitation and an impurity mode. [6] These characteristics of soliton scattering from an attractive well are generic and apply also to Sine-Gordon solitons and perhaps even other solitons, not researched until now.…”

Phonon emission from a discrete sine-Gordon breather

“…In the last few decades it has been demonstrated that di erent kinds of perturbations give rise to many interesting phenomena (see e.g., Refs. [4,5] and references therein). For the nonintegrable systems various resonance e ects may take place [5±11].…”