Related papers: A discrete phi^4 system without Peierls-Nabarro ba…
In this paper, we study the single kink and the kink-antikink collisions of a nonlinear beam equation bearing a fourth-derivative term. We numerically explore some of the key characteristics of the single kink both in its standing wave and…
We analyze the effect of internal degrees of freedom on the movability properties of localized excitations on defect-free nonlinear Hamiltonian lattices by means of properties of a local phase space which is at least of dimension six. We…
A lattice Boltzmann model for amphiphilic fluid dynamics is presented. It is a ternary model, in that it conserves mass separately for each chemical species present (water, oil, amphiphile), and it maintains an orientational degree of…
In the present paper, a discrete differential calculus is introduced and used to describe dynamical systems over arbitrary graphs. The discretization of space and time allows the derivation of Heisenberg-like uncertainty inequalities and of…
We study localization, pinning, and mobility in the fractional discrete nonlinear Schr\"odinger equation (fDNLS) with generalized power-law coupling. A finite-dimensional spatial-dynamics reduction of the nonlocal recurrence yields onsite…
Nonlinear mechanical metamaterials can exhibit emergent transport phenomena that mimic topological protection without relying on linear band topology. Here, we realize a bifurcation-induced nonreciprocal lattice that supports robust…
In a classical, quartic field theory with $SU(N) \times Z_2$ symmetry, a class of kink solutions can be found analytically for one special choice of parameters. We construct these solutions and determine their energies. In the limit $N\to…
A class of discrete nonlinear Schrodinger equations with arbitrarily high order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the…
We discuss the process by which energy, initially evenly distributed in a nonlinear lattice, can localize itself into large amplitude excitations. We show that, the standard modulational instability mechanism, which can initiate the process…
In this paper, we numerically study the scattering of kinks in the noncanonical sine-Gordon model using Fourier spectral methods. The model depends on two free parameters, which control the localized inner structure in the energy density…
A finite element discretization using a method of lines approached is proposed for approximately solving the Poisson-Nernst-Planck (PNP) equations. This discretization scheme enforces positivity of the computed solutions, corresponding to…
A quench in an overdamped one dimensional $\phi^4$ model is studied by analytical and numerical methods. For an infinite system or a finite system with free boundary conditions, the density of kinks after the transition is proportional to…
We investigate the strong coupling region of the topological sector of the two-dimensional $\phi^4$ theory. Using discrete light cone quantization (DLCQ), we extract the masses of the lowest few excitations and observe level crossings. To…
In this work we consider kink-antikink and antikink-kink collisions in a modified $\phi^4$ model with a false vacuum characterized by a dimensionless parameter $\epsilon$. The usual $\phi^4$ model is recovered for $\epsilon=0$. We…
We study the dynamics of hardcore spin models on the square and triangular lattice, constructed by analogy to hard spheres, where the translational degrees of freedom of the spheres are replaced by orientational degrees of freedom of spins…
We borrow the form of potential of the well-known kink-bearing $\varphi^4$ system in the range between its two vacua and paste it repeatedly into the other ranges to introduce the periodic $\varphi^4$ system. The paper is devoted to…
We propose a new mechanism of long-range coupling to excite low-frequency discrete breathers without the on-site potential. This mechanism is universal in long-range systems irrespective of the spatial boundary conditions, of topology of…
Many solitonic configurations in field theory have localized bound states in their spectrum of linear perturbations. This opens up the possibility of having long lived excitations of these solitons that could affect their dynamics. We start…
Motivated by the normal form of a fast-slow ordinary differential equation exhibiting a pitchfork singularity we consider the discrete-time dynamical system that is obtained by an application of the explicit Euler method. Tracking…
In a prior paper the authors obtained a four-dimensional discrete integrable dynamical system by the traveling wave reduction from the lattice super-KdV equation in a case of finitely generated Grassmann algebra. The system is a coupling of…