相关论文: Third-order integrable difference equations genera…
We derive a set of bilinear functional equations of Hirota type for the partition functions of the $sl(2)$ related integrable statistical models defined on a random lattice. These equations are obtained as deformations of the Hirota…
The computation of perturbative corrections to processes involving heavy quarks is crucial for the precision program of the LHC and future colliders. In this article, we describe a powerful approach to calculate higher-orders in QCD…
In recent years, progress toward the classification of superintegrable systems with higher order integrals of motion has been made. In particular, a complete classification of all exotic potentials with a third or a fourth order integrals,…
We consider arithmetic three-spheres inequalities to solutions of certain second order quasilinear elliptic differential equations and inequalities with a Riccati-type drift term.
The q-Hermite I-Sobolev type polynomials of higher order are consider for their study. Their hypergeometric representation is provided together with further useful properties such as several structure relations which give rise to a…
We investigate existence of solitonic solutions for higher-order partial differential equations with polynomial nonlinearities. Using the Hirota method we obtain classification for higher-order integrable systems of equations.
Nonlinear parabolic equations are central to numerous applications in science and engineering, posing significant challenges for analytical solutions and necessitating efficient numerical methods. Exponential integrators have recently…
Runge-Kutta methods have an irreplaceable position among numerical methods designed to solve ordinary differential equations. Especially, implicit ones are suitable for approximating solutions of stiff initial value problems. We propose a…
Many practical problems can be described by second-order system $\ddot{q}=-M\nabla U(q)$, in which people give special emphasis to some invariants with explicit physical meaning, such as energy, momentum, angular momentum, etc. However,…
Explicit relations of matrices for two-dimensional finite element method with third-order triangular elements are given. They are more simple than relations presented in other works and could be easily implemented in new algorithms for both…
Product formula methods, particularly the second-order Suzuki decomposition, are an important tool for simulating quantum dynamics on quantum computers due to their simplicity and unitarity preservation. While higher-order schemes have been…
A class of high-order numerical algorithms for Riesz derivatives are established through constructing new generating functions. Such new high-order formulas can be regarded as the modification of the classical (or shifted) Lubich's…
Three comparison criteria are obtained for second order Riccati equations. On the basis of these criteria some global existence theorems are proved mentioned equations. The results obtained are used to derive a non oscillation criterion for…
We propose a direct measure of tripartite quantum correlation in an arbitrary symmetric pure state of N correlated two-level atoms (qubits). We compute the third order moments of the collective pseudo-spin operators in terms of the…
Delay-differential equations are functional differential equations that involve shifts and derivatives with respect to a single independent variable. Some integrability candidates in this class have been identified by various means. For…
In this brief, we discuss the implementation of a third order semi-implicit differentiator as a complement of the recent work by the author that proposes an interconnected semi-implicit Euler double differentiators algorithm through Taylor…
Superposition rules form a class of functions that describe general solutions of systems of first-order ordinary differential equations in terms of generic families of particular solutions and certain constants. In this work we extend this…
Quantum superintegrable systems are solvable eigenvalue problems. Their solvability is due to symmetry, but the symmetry is often "hidden". The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation…
A wide range of implicit time integration methods, including multi-step, implicit Runge-Kutta, and Galerkin finite-time element schemes, is evaluated in the context of chaotic dynamical systems. The schemes are applied to solve the Lorenz…
Whereas Lie had linearized scalar second order ordinary differential equations (ODEs) by point transformations and later Chern had extended to the third order by using contact transformation, till recently no work had been done for higher…