Related papers: Long-range interacting solitons: pattern formation…
Enhanced experimental capabilities to control nonlocal and power-law decaying interactions are currently fuelling intense research in the domain of quantum many-body physics. Compared to their counterparts with short-ranged interactions,…
The aim of this paper is to provide a construction of stationary discrete solitons in an extended one-dimensional Discrete NLS model with non-nearest neighbour interactions. These models, models of the type with long-range interactions were…
This survey offers an overview of recent advances in nonlocal phase transition problems, modeled by Ginzburg--Landau type energies of the form \[ \frac{1}{4}\iint_{\R^{2n}\setminus (\R^n \setminus \Omega)^2}…
We establish the long time soliton asymptotics for the translation invariant nonlinear system consisting of the Klein-Gordon equation coupled to a charged relativistic particle. The coupled system has a six dimensional invariant manifold of…
We prove the Lieb-Schultz-Mattis theorem in $d$-dimensional spin systems exhibiting $SO(3)$ spin rotation and lattice translation symmetries in the presence of $k-$local interactions decaying as $\sim 1/r^\alpha$ with distance $r$. Two…
We demonstrate that linear degeneracy is a necessary condition for quasilinear systems of Jordan block type to possess first-order Hamiltonian structures. Multi-Hamiltonian formulation of linearly degenerate systems governing…
We consider KdV-type equations with $C^1$ nonhomogeneous nonlinearities and small dispersion $\varepsilon$. The first result consists in the conclusion that, in the leading term with respect to $\varepsilon$, the solitary waves in this…
In this chapter we review recent results concerning localized and extended dissipative solutions of the discrete complex Ginzburg-Landau equation. In particular, we discuss discrete diffraction effects arising both from linear and nonlinear…
A general method to find an effective potential of interaction between far separated 2D and 3D solitons is elaborated, including the case of 2D vortex solitons. The method is based on explicit calculation of the overlapping term in the full…
We present a simple model of interaction of the Maxwell equations with a matter field defined by the Klein-Gordon equation. A simple linear interaction and a nonlinear perurbation produce solutions of the equations containing hylomorphic…
We present an analytical and numerical study of the Klein-Gordon kink-soliton dynamics in inhomogeneous media. In particular, we study an external field that is almost constant for the whole system but that changes its sign at the center of…
Thermodynamic and dynamical properties of systems with long-range pairwise interactions (LRI), which decay as $1/r^{d+\sigma}$ at large distances $r$ in $d$ dimensions, are reviewed. Two broad classes of such systems are discussed. (i)…
We consider the realization of N=2 superconformal models in terms of free first-order $(b,c,\beta,\gamma)$-systems, and show that an arbitrary Landau-Ginzburg interaction with quasi-homogeneous potential can be introduced without spoiling…
We consider a finite but arbitrarily large Klein-Gordon chain, with periodic boundary conditions. In the limit of small couplings in the nearest neighbor interaction, and small (total or specific) energy, a high order resonant normal form…
Short-range corrections to long-range selected configuration interaction calculations are derived from perturbation theory considerations and applied to harmonium (with two to six electrons for some low-lying states). No fitting to…
We investigate the long-time dynamics of the Sine-Gordon (SG) model under a class of perturbations whose quantum field theoretic analog - via bosonization - corresponds to the massive Schwinger model describing 1+1D relativistic QED of…
The kinetic energy term of Hamiltonian systems with balanced loss and gain is not semi-positive-definite, leading to instabilities at the classical as well quantum level. It is shown that an additional Lorentz interaction in the Hamiltonian…
The ability to tailor the hopping interactions between the constituent elements of a physical system could enable the observation of unusual phenomena that are otherwise inaccessible in standard settings. In this regard, a number of recent…
In additional to the parity ($\mathcal{P}$) symmetric, time reversal ($\mathcal{T}$) symmetric, and $\mathcal{PT}$ symmetric nonlocal integrable systems, some other types of nonlocal integrable Klein-Gordon models with the space-time…
We introduce a model which integrates the complex Ginzburg-Landau (CGL) equation in two dimensions (2D) with the linear-cubic-quintic combination of loss and gain terms, self-defocusing nonlinearity, and a periodic potential. In this…