Related papers: Equations of 3-th waves hierarchy
Two Dunkl oscillator models are considered: one singular and the other with a 2:1 frequency ratio. These models are defined by Hamiltonians which include the reflection operators in the two variables x and y. The singular or caged Dunkl…
Discrete gradient methods are a powerful tool for the time discretization of dynamical systems, since they are structure-preserving regardless of the form of the total energy. In this work, we discuss the application of discrete gradient…
A new relativistic description of quantum electrodynamics is presented. Guideline of the theory is the Klein-Gordon equation, which is reformulated to consider spin effects. This is achieved by a representation of relativistic vectors with…
Canonical analysis leading to formal quantisation of the higher derivative theories are considered. The first order formalism is adopted where all the configuration space variables along with their higher time derivatives are considered to…
Calculations of the leading quantum electrodynamics effects in few electron systems involve singular matrix elements of the inter-electronic distances of the form $1/r_i^3$ and $1/r_{ij}^3$. Integrals that result when the nonrelativistic…
Supersymmetry transformations of first and second order are used to generate Hamiltonians with known spectra departing from the harmonic oscillator with an infinite potential barrier. It is studied also the way in which the eigenfunctions…
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general associative cubic algebra and we present specific…
Most non-relativistic interacting quantum many-body systems, such as atomic and molecular ensembles or materials, are naturally described in terms of continuous-space Hamiltonians. The simulation of their ground-state properties on digital…
In this paper, we provide a simple method to generate higher order position solutions and rogue wave solutions for the derivative nonlinear Schr\"odinger equation. The formulae of these higher order solutions are given in terms of…
The classical numerical methods play important roles in solving wave equation, e.g. finite difference time domain method. However, their computational domain are limited to flat space and the time. This paper deals with the description of…
Motivated by the study of uniaxial crystal optics, we consider a coupled system of $3D$ anisotropic wave equations, in which they have the same speed only in one direction but distinct speeds in the other directions. Moreover, this system…
This paper is concerned with the final value problem for a system of nonlinear wave equations. The main issue is to solve the problem for the case where the nonlinearity is of a long range type. By assuming that the solution is spherically…
An effective method for generating linear equations of maximal symmetry in their much general normal form is obtained. In the said normal form, the coefficients of the equation are differential functions of the coefficient of the term of…
We study the bi-Hamiltonian structures for the hierarchy of a 3-component generalization of the Degasperis-Procesi (3-DP) equation. We show that all Hamiltonian functionals in the hierarchy are homogenous, and Hamiltonian functionals of the…
We develop the Hamiltonian theory of axial perturbations around a general time-dependent spherical background spacetime. Using the fact that the linearized constraints are gauge generators, we isolate the physical and unconstrained axial…
We study Hamiltonian difference schemes for scalar conservation laws with monotone flux function and establish the existence of a three-parameter family of periodic travelling waves (wavetrains). The proof is based on an integral equation…
It is expected that the quantum nature of spacetime leaves its imprint in all semiclassical gravitational systems, at least in certain regimes, including gravitational waves. In this paper we investigate such imprints on gravitational waves…
Discrete gradient methods are a class of numerical integrators producing solutions with exact preservation of first integrals of ordinary differential equations. In this paper, we apply order theory combined with the symmetrized Itoh--Abe…
In addition to the usual linear gravitational waves in transverse-traceless coordinates, higher-order gravitational field equations, as well as their corresponding solutions, are explicitly obtained. It is found that higher-order waves do…
In this paper, we study the adaptive planewave discretization for a cluster of eigenvalues of second-order elliptic partial differential equations. We first design an a posteriori error estimator and prove both the upper and lower bounds.…