Related papers: Analytical Approximate Solution of a Coupled Two F…
An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture…
Analytical solution of precise equations that describe the rf-coupling of two cavities through a co-axial cylindrical hole are given for various limited cases. For their derivation we have used the method of solution of an infinite set of…
We introduce a method based on auxiliary master equation for solving the problem of an impurity with local electron-electron and electron-phonon interaction embedded between two conduction leads with a finite bias voltage. The…
This paper presents an analytical formulation for correcting the diffraction associated to the second harmonic of an acoustic wave, more compact than that usually used. This new formulation, resulting from an approximation of the correction…
The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in…
Approximating periodic solutions to the coupled Duffing equations amounts to solving a system of polynomial equations. The number of complex solutions measures the algebraic complexity of this approximation problem. Using the theory of…
We consider two heteronuclear atoms interacting with a short-range $\delta$ potential and confined in a ring trap. By taking the Bethe-ansatz-type wavefunction and considering the periodic boundary condition properly, we derive analytical…
The auxiliary field method is a new technique to obtain closed formulae for the solutions of eigenequations in quantum mechanics. The idea is to replace a Hamiltonian $H$ for which analytical solutions are not known by another one $\tilde…
We show that the two couple equations derived by approximate symmetry method and approximate homotopy symmetry method are connected by a transformation for the perturbed PDEs. Consequently, approximate homotopy series solutions can be…
The non-integrability of the Hill problem makes that its global dynamics must be necessarily approached numerically. However, the analytical approach is feasible in the computation of relevant solutions. In particular, the nonlinear…
By either performing a Taylor expansion or making a polynomial approximation, the Bethe equation for charged particle stopping power in matter can be integrated analytically to obtain the range of charged particles in the continuous…
We have carried out an approximate analytical solution to precisely consider the influence of magnetic field on the transverse oscillation of particles in cyclotron. The differential equations of transverse oscillation are solved from the…
Developing an analytical theory for atomic coherence driven by ultrashort laster pulses has proved to be challenging due to the breakdown of the rotating wave approximation (RWA). In this paper, we present an approximate, closed-form…
The Dirac equation for H$_2^+$ is solved numerically using an iterative method proposed by Kutzelnigg [Z. Phys. 11, 15 (1989]. The four-component wavefunction is expanded in a newly introduced kinetically balanced exponential basis set. The…
In this article, we discuss quantitative Runge approximation properties for the acoustic Helmholtz equation and prove stability improvement results in the high frequency limit for an associated partial data inverse problem modelled on…
We obtain exact solutions of the Klein-Gordon and Pauli Schroedinger equations for a two-dimensional hydrogen-like atom in the presence of a constant magnetic field. Analytic solutions for the energy spectrum are obtained for particular…
In the first part of the paper, we propose and rigorously analyze a mixed finite element method for the approximation of the periodic strong solution to the fully nonlinear second-order Hamilton--Jacobi--Bellman equation with coefficients…
We generalize stochastic resonance to the nonadiabatic limit by treating the double-well potential using two quadratic potentials. We use a singular perturbation method to determine an approximate analytical solution for the probability…
We describe a procedure to solve an up to $2N$ problem where the particles are separated topologically in $N$ groups with at most two particles in each. Arbitrary interactions are allowed between the (two) particles within one group. All…
Numerical solution of one-dimensional stochastic integral equations because of the randomness has its own problems, i.e. some of them no have analytically solution or finding their analytic solution is very difficult. This problem for…