相关论文: Reduction of static field equation of Faddeev mode…

The authors of the article Phys. Lett. B 652 (2007) 384, (arXiv:0707.2207), propose an interesting method to solve the Faddeev model by reducing it to a set of first order PDEs. They first construct a vectorial quantity $\bm \alpha $,…

An application of the equation proposed by the present authors, which is equivalent to the static field equation of the Faddeev model, is discussed. Under some assumptions on the space and on the form of the solution, the field equation is…

Faddeev' equations are a set-theoretical and an operator forms of the star-triangle equation. Known solutions of the quantum star-triangle equation, related to the Faddeev equations, are based on various forms of the modular double of the…

We investigate the presence of static solutions in models described by real scalar field in two-dimensional spacetime. After taking advantage of a procedure introduced sometime ago, we solve intricate nonlinear ordinary differential…

We propose the symmetry reduction method of partial differential equations to the system of differential equations with fewer number of independent variables. We also obtain generalized sufficient conditions for the solution found by…

Applying proper orthogonal decomposition to a usual finite element (FE) formulation for space fractional partial differential equation, we get a reduced FE model, which greatly reduces the complexity of computation. Then, the stability…

A new method for derivation of the equation of motion from the field equation is proposed. The problem of embedding the singularities in a field satisfying the field equations is discussed.

The formal scattering theory is developed for the three-particle differential Faddeev equations. The theory is realised along the same line as in the standard two-body case. The solution of the scattering problem is expressed in terms of…

The Faddeev technique is employed to address the problem of describing the influence of both particle-particle and particle-hole phonons on the single-particle self-energy. The scope of the few-body Faddeev equations is extended to describe…

We present a method to obtain soliton solutions to relativistic system of coupled scalar fields. This is done by examining the energy associated to static field configurations. In this case we derive a set of first-order differential…

Phase field equations describe the novel approach to the Stefan problems. We calculate these equations numerically performed in two-dimensions. We take full advantage of the phase field parameter $\varphi$ to track the interface on which…

Numerical solving differential equations with fractional derivatives requires elimination of the singularity which is inherent in the standard definition of fractional derivatives. The method of integration by parts to eliminate this…

A solution of the Einstein vacuum field equations is constructed within the contex of perturbation theory. The solution possesses a graphical representation in terms of diagrams.

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order…

In many nonlinear field theories, relevant solutions may be found by reducing the order of the original Euler-Lagrange equations, e.g., to first order equations (Bogomolnyi equations, self-duality equations, etc.). Here we generalise,…

We shortly recall the derivation of the Faddeev-Yakubovsky differential equations and point out their main advantages. Then we give a review of the numerical approaches used to solve the bound-state and scattering problems for the three-…

The main aim of this paper is the investigation of the stability problem for ordinary delay differential equations. More precisely, we would like to study the following problem. Assume that for a continuous function a given delay…

We present a new discretization for the Hadamard fractional derivative, that simplifies the computations. We then apply the method to solve a fractional differential equation and a fractional variational problem with dependence on the…

A novel approach to solve the Faddeev equation for three-body scattering at arbitrary energies is proposed. This approach disentangles the complicated singularity structure of the free three-nucleon propagator leading to the moving and…

The numerical solution methods for partial differential equation (PDE) solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods…