Related papers: Lattice equations and their solutions with complex…
In this paper, we investigate the lifespan estimates of classical solutions of the initial value problems for semilinear wave equations of derivative type with characteristic weights in one space dimension. Such equations provide us basic…
The purpose of this paper is to further exemplify an approach to evolutionary problems originally developed in earlier works for a special case and later extended to more general evolutionary problems. We are here concerned with the $(1+1)$…
In a series of recent papers we have shown how the dynamical behavior of certain classical systems can be analyzed using operators evolving according to Heisenberg-like equations of motions. In particular, we have shown that raising and…
We propose an unconventional formulation of lattice field theories which is quite general, although originally motivated by the quest of exact lattice supersymmetry. Two long standing problems have a solution in this context: 1) Each degree…
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…
A class of linear evolutionary equations with material laws involving fractional time-derivatives is considered. The main result is well-posedness and causality for this problem class. The approach is illustrated with two examples: a…
We present a set of polynomial equations that provides models of the lattice Boltzmann theory for any required level of accuracy and for any dimensional space in a general form. We explicitly derive two- and three-dimensional models…
Invariance under translation is exploited to efficiently simulate one-dimensional quantum lattice systems in the limit of an infinite lattice. Both the computation of the ground state and the simulation of time evolution are considered.
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…
We study the hypoellipticity and solvability properties of a class of time-periodic evolution operators, with coefficients globally defined on $\mathbb{R}^d$ and growing polynomially with respect to the space variable. To this aim, we…
In this paper we consider evolution equations in the abstract Hilbert space under the special conditions imposed on the operator at the right-hand side of the equation. We establish the method that allows us to formulate the existence and…
Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Due to instabilities, small…
The spectrum of masses from a lattice QCD simulation may be found by fitting exponential functions to correlators of operators possessing the quantum numbers of the particles of interest. The ability of evolutionary algorithms to find…
We study complexity in terms of degree growth of one-component lattice equations defined on a $3\times 3$ stencil. The equations include two in Hirota bilinear form and the Boussinesq equations of regular, modified and Schwarzian type.…
By introducing a kind of special functions namely exponent-like function, cosine-like function and sine-like function, we obtain explicitly the basic structures of solutions of initial value problem at the original point for this kind of…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
We provide a simple method to recognize classical orthogonal polynomials on lattices defined only by their coefficients of the three term recurrence relation.
We consider time periodic Hamiltonians with complex potentials on the lattice and determine trace formulas. As a corollary we estimate eigenvalues of the quasienergy operator in terms of the norm of potentials.
The relativistic formulation of abstract evolution equations is introduced. The corresponding logarithmic representation is shown to exist without assuming the invertible property of evolution operators. Consequently, by means of the…
We discuss linear autonomous evolution equations on function spaces which have the property that a positive initial value leads to a solution which initially changes sign, but then becomes - and stays - positive again for sufficiently large…