Related papers: Explicit Solutions for a Nonlinear Vector Model on…
We present what we believe to be the first known example of an exact quasiperiodic localized stable solution with spatially symmetric large-amplitude oscillations in a non-integrable Hamiltonian lattice model. The model is a one-dimensional…
We study variable-rate linear quenches in the anisotropic Heisenberg (XXZ) chain, starting at the XX point. This is equivalent to switching on a nearest neighbour interaction for hard-core bosons or an interaction quench for free fermions.…
In this paper we study sequences of vector orthogonal polynomials. The vector orthogonality presented here provides a reinterpretation of what is known in the literature as matrix orthogonality. These systems of orthogonal polynomials…
In the present paper, we study spin-${1 \over 2}$ antiferromagnetic (AF) Heisenberg model on layered anisotropic triangular lattice and obtain its phase structure. We use the Schwinger bosons for representing spin operators and also…
Fullerenes and nanotubes consist of a large number of carbon atoms sitting on the sites of a regular lattice. For pratical reasons it is often useful to approximate the equations on this lattice in terms of the continuous equation. At the…
We investigate the connection between the linear harmonic oscillator equation and some classes of second order nonlinear ordinary differential equations of Li\'enard and generalized Li\'enard type, which physically describe important…
In this paper, we present a novel method to compute an explicit formula for the inverse of the confluent Vandermonde matrices. Our proposed results may have many interesting perspectives in diverse areas of mathematics and natural sciences,…
The direct linearization structure is presented of a "mild" but significant generalization of the lattice BSQ system. Some of the equations in this system were recently discovered in [J. Hietarinta, J. Phys {\bf A}: Math. Theor. {\bf 44}…
In this paper we formulate a new N-state spin integrable model on a three-dimensional lattice with spins interacting round each elementary cube of the lattice. This model can be also reformulated as a vertex type model. Weight functions of…
Miscellaneous magnetic systems are being recently intensively investigated because of their potential applications in modern technologies. Nonetheless, a many body dynamical description of complex magnetic systems may be cumbersome,…
We study a class of linearly coupled system of quasilinear equations. Under some assumptions on the nonlinear terms, we establish some results about the existence and regularity of vector solutions for the p-Laplacian systems by using…
The uniform two-dimensional variational tensor product state is applied to the transverse-field Ising, XY, and Heisenberg models on a regular hyperbolic lattice surface. The lattice is constructed by tessellation of the congruent pentagons…
In the present paper an introduction to the new subject of nonlinear dispersive hamiltonian equations on graphs is given. The focus is on recently established properties of solutions in the case of nonlinear Schr\"odinger equation. Special…
We present an exact solution for an asymmetric exclusion process on a ring with three classes of particles and vacancies. Using a matrix product Ansatz, we find explicit expressions for the weights of the configurations in the stationary…
Inspired by large applications of topological defects in describing different phenomena in physics, and considering the importance of three dimensional solutions in AdS/CFT correspondence, in this paper we obtain magnetic anti-de Sitter…
Aim of this paper is the qualitative analysis of the solution of a boundary value problem for a third-order non linear parabolic equation which describes several dissipative models. When the source term is linear, the problem is explictly…
By using a simulated annealing approach, Monte Carlo and molecular-dynamics techniques we have studied static and dynamic behavior of the classical two-dimensional anisotropic Heisenberg model. We have obtained numerically that the vortex…
We show how to construct a non-smooth solution to Hessian fully nonlinear second-order uniformly elliptic equation using the Cartan isoparametric cubic in 5 dimensions.
We obtain a new solution to the star-triangle relation for an Ising-type model with two kinds of spin variables at each lattice site, taking continuous real values and arbitrary integer values, respectively. The Boltzmann weights are…
In this letter, we study the purely nonlinear oscillator by the method of action-angle variables of Hamiltonian systems. The frequency of the non-isochronous system is obtained, which agrees well with the previously known result. Exact…