Shape and wobbling wave excitations in Josephson junctions: Exact solutions of the(2+1)-dimensional sine-Gordon model

Sine-Gordon wobbles through Bäcklund transformations

“…where V s and U s are given by ( 17) and (18), respectively. It is clear that the wobble solution ( 16)- (18) follows from ( 26) and ( 29).…”

“…There are also oscillatory, non-topological solutions called breathers, which are bound states of a kink and an antikink. Yet another solution is the "wobble", which can be interpreted as a nonlinear superposition of a kink and a breather [36,5,18].Among these models, the sine-Gordon (sG) equation,differs from the others in being an integrable system. An infinite number of conservation laws [22,35,37], elastic interaction among solitons [38,8,14], existence of…”

“…There are also oscillatory, non-topological solutions called breathers, which are bound states of a kink and an antikink. Yet another solution is the "wobble", which can be interpreted as a nonlinear superposition of a kink and a breather [36,5,18].…”

Study of the two‐dimensional sine‐Gordon equation arising in Josephson junctions using meshless finite point method

“…The SG equation also describes the deformation of a nonlinear crystal lattice, properties of Bloch walls in ferromagnets, propagation of pulses in 2‐level resonance mediums, the orientation structure of liquid crystals, commensurability‐noncommensurability phase transitions, in molecular biology, information transport in microtubules, nonlinear optics and high‐temperature superconductors, etc . Also see Gulevich et al and the references therein for more details. The three‐dimensional SG equation in spherical symmetry mostly has been considered as a model for nonlinear field theories .…”

Array of Josephson junctions with a nonsinusoidal current-phase relation as a model of the resistive transition of unconventional superconductors

“…and intrinsic Josephson junctions in cuprates are considered as prominent examples.In polycrystalline superconductors in the vicinity of the transition, nonequilibrium effects make the relevant properties of the weak-links spatially and temporally dependent on the external drive16,[29][30][31][32][33] . Hence, when a polycrystalline superconductor undergoes the transition, the onset of higher harmonics may occur according to the local voltage, geom-etry and chemistry of the grains.…”