Related papers: Discrete soliton ratchets driven by biharmonic fie…
We establish the full asymptotic stability of the sine-Gordon kink outside symmetry under small perturbations in weighted Sobolev norms. Our proof consists of a space-time resonances approach based on the distorted Fourier transform to…
Extending a recent effective theory formulation for the dynamics of kinks in the sine-Gordon model [1], we propose an analogous effective description of $\phi^4$ kinks. Three different reduced models based on the kink position, width and…
We use a two-state ratchet model to study the cooperative bidirectional motion of molecular motors on cytoskeletal tracks with randomly alternating polarities. Our model is based on a previously proposed model [Badoual et al., {\em Proc.…
We consider a prototypical model in which a nonlinear field (continuum or discrete) evolves on a flexible substrate which feeds back to the evolution of the main field. We identify the underlying physics and potential applications of such a…
We put forward properties of solitons supported by optical lattices featuring topological dislocations, and show that solitons experience attractive and repulsive forces around the dislocations. Suitable arrangements of dislocations are…
Soliton dynamics in spin-textured metals generate electrical currents, which produce backaction through spin torques. We modify the Landau-Lifshitz-Gilbert equation and the corresponding solitonic equations of motion to include such…
The electric resistivity is examined in the constrained Hilbert space of a doped Mott insulator, which is dictated by a non-Ioffe-Larkin composition rule due to the underlying mutual Chern-Simons topological gauge structure. In the…
Using a particle-based model, we simulate the behavior of a skyrmion under the influence of asymmetric funnel geometries and ac driving at zero temperature. We specifically investigate possibilities for controlling the skyrmion motion by…
It is well-known that localized topological defects (solitons) experience recoil when they suffer an impact by incident particles. Higher-dimensional topological defects develop distinctive wave patterns propagating along their worldvolume…
While fundamental-mode discrete solitons have been demonstrated with both self-focusing and defocusing nonlinearity, high-order-mode localized states in waveguide lattices have been studied thus far only for the self-focusing case. In this…
We study (2+1)-dimensional multicomponent spatial vector solitons with a nontrivial topological structure of their constituents, and demonstrate that these solitary waves exhibit a symmetry-breaking instability provided their total…
We demonstrate the operation of a quantum ratchet in the absence of dissipative processes within the observation time (Hamiltonian regime). An atomic rubidium Bose-Einstein condensate is exposed to a sawtooth-like optical lattice potential,…
We investigate mobility regimes for localized modes in the discrete nonlinear Schr\"{o}dinger (DNLS) equation with the cubic-quintic onsite terms. Using the variational approximation (VA), the largest soliton's total power admitting…
Solitons in space-time capable of transporting time-like observers at superluminal speeds have long been tied to violations of the weak, strong, and dominant energy conditions of general relativity. This trend was recently broken by a new…
An ensemble of particles in thermal equilibrium at temperature $T$, modeled by Nos\`e-Hoover dynamics, moves on a triangular lattice of oriented semi-disk elastic scatterers. Despite the scatterer asymmetry a directed transport is clearly…
We theoretically propose the emergence of nonlinear nonreciprocal conductivity in centrosymmetric paramagnetic systems when a spatially gradient magnetic field is externally applied. The key essence lies in the appearance of magnetic…
The statics, stability and dynamical properties of dark-bright soliton pairs are investigated motivated by applications in a homogeneous system of two-component repulsively interacting Bose-Einstein condensate. One of the intra-species…
In theories where spacetime is a direct product of Minkowski space ($M^4$) and a d dimensional compact space ($K^d$), there can exist topological solitons that simultaneously wind around $R^3$ (or $R^2$ or $R^1$) in $M^4$ and the compact…
We analyze the dynamics of a classical particle in a spatially periodic potential under the influence of a periodic in time uniform force. It was shown in [S.Flach, O.Yevtushenko, Y. Zolotaryuk, Phys. Rev. Lett. 84, 2358 (2000)] that…
We propose and study a novel way to produce a DC transport of vortices when applying an AC electrical current to a sample. Specifically, we study superconductors with a graduated random pinning density, which transports interacting vortices…