Related papers: Snakes in square, honeycomb, and triangular lattic…
We report results of systematic analysis of various modes in the flatband lattice, based on the diamond-chain model with the on-site cubic nonlinearity, and its double version with the linear on-site mixing between the two lattice fields.…
We present a thorough analysis of soliton solutions to the quasi-one-dimensional nonlinear Dirac equation (NLDE) for a Bose-Einstein condensate in a honeycomb lattice with armchair geometry. Our NLDE corresponds to a quasi-one-dimensional…
Homoclinic snaking is a widespread phenomenon observed in many pattern-forming systems. Demonstrating its occurrence in non-perturbative regimes has proven difficult, although a forcing theory has been developed based on the identification…
In this paper we prove the uniqueness of the saddle-shaped solution to the semilinear nonlocal elliptic equation $(-\Delta)^\gamma u = f(u)$ in $\mathbb R^{2m}$, where $\gamma \in (0,1)$ and $f$ is of Allen-Cahn type. Moreover, we prove…
We consider a tight-binding model on the regular honeycomb lattice with uncorrelated on-site disorder. We use two independent methods (recursive Green's function and self-consistent Born approximation) to extract the scattering mean free…
We address the existence and stability of localized modes in the two-dimensional (2D) linear Schroedinger lattice with two symmetric nonlinear sites embedded into it, and a generalization for moderately localized nonlinearity featuring two…
Numerical simulations of the complex cubic-quintic Ginzburg-Landau equation (CCQGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal five entirely novel classes…
I introduce a new type of continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First I analyze the quantum snake walk on the line, and I…
The correlations in the motion of reptating polymers in their melt are investigated by means of kinetic Monte Carlo simulations of the three dimensional slithering snake version of the bond-fluctuation model. Surprisingly, the slithering…
In this theoretical study, we present an analytical framework to investigate the slithering motion of snakes on flat surfaces. While previous studies have predominantly relied on numerical methods to identify optimal locomotion kinematics,…
We consider the two-dimensional Fermi-Pasta-Ulam lattice with hexagonal honeycomb symmetry, which is a Hamiltonian system describing the evolution of a scalar-valued quantity subject to nearest neighbour interactions. Using multiple-scale…
We perform bifurcation analysis of plane wave solutions in one-dimensional cubic-quintic Ginzburg-Landau equation with delayed feedback. Our study reveals how multistability and snaking behavior of plane waves emerge as time delay is…
This paper studies the existence of multiple non-trivial stationary solutions of a partial differential equation (PDE) model introduced in [3], motivated by collective ant behavior. Previous work suggested the presence of two types of…
Lattice animals provide a discretized model for the theta transition displayed by branched polymers in solvent. Exact graph enumeration studies have given some indications that the phase diagram of such lattice animals may contain two…
We model the electronic properties of thin films of binary compounds with stacked layers where each layer is a two-dimensional honeycomb lattice with two atoms per unit cell. The two atoms per cell are assigned different onsite energies in…
The "snake" is a persistent density perturbation at the rational q-surfaces after pellet injection. Together with other phenomena (density pinch and profile resiliancy) it can be traced back to the extremum of an action functional for…
Snake graphs appear naturally in the theory of cluster algebras. For cluster algebras from surfaces, each cluster variable is given by a formula which is parametrized by the perfect matchings of a snake graph. In this paper, we continue our…
Invariant solutions of shear flows have recently been extended from spatially periodic solutions in minimal flow units to spatially localized solutions on extended domains. One set of spanwise-localized solutions of plane Couette flow…
We consider the symmetry-breaking steady state bifurcation of a spatially-uniform equilibrium solution of E(2)-equivariant PDEs. We restrict the space of solutions to those that are doubly-periodic with respect to a square or hexagonal…
We study the structure of the solution space and behavior of local search methods on random 3-SAT problems close to the SAT/UNSAT transition. Using the overlap measure of similarity between different solutions found on the same problem…