We study linear stochastic evolution partial differential equations driven by additive noise. We present a general and flexible framework for representing the infinite dimensional Wiener process which is driving the equation. Since the eigenfunctions and eigenvalues of the covariance operator of the process are usually not available for computations, we propose an expansion in an arbitrary fram...

An accidental degeneracy of resonances gives rise to a double pole in the scattering matrix, a double zero in the Jost function and a Jordan chain of length two of generalized Gamow-Jordan eigenfunctions of the radial Schrödinger equation. The generalized Gamow-Jordan eigenfunctions are basis elements of an expansion in bound and resonant energy eigenfunctions plus a continuum of scattering wav...

in this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. furthermore, we obtain the zeros of eigenfunctions.

In this paper, based on Kelvin and Linear Standard Solid models, dynamic response and the buckling load of a viscoelastic beam under  lateral and axial loads have been determined. The governing equations have been extracted using Euler  and Timoshenko theories and their analytical solutions have been obtained by using the eigenfunctions expansion method. Buckling load have been calculated by us...

The linearized Vlasov equation for a plasma system in a uniform magnetic field and the corresponding linear Vlasov operator are studied. The spectrum and the corresponding eigenfunctions of the Vlasov operator are found. The spectrum of this operator consists of two parts: one is continuous and real; the other is discrete and complex. Interestingly, the real eigenvalues are infinitely degenerat...

This paper considers a nonlinear dynamical system on a complex, finite dimensional Banach space which has an asymptotically stable, hyperbolic fixed point. We investigate the connection between the so-called principle eigenfunctions of the Koopman operator and the existence of a topological conjugacy between the nonlinear dynamics and its linearization in the neighborhood of the fixed point. Th...

In this article, we present the analytical solution of the radial Schrödinger equation for the Hulthén potential within the framework of the asymptotic iteration method by using an approximation to the centrifugal potential for any l states. We obtain the energy eigenvalues and the corresponding eigenfunctions for different screening parameters. The wave functions are physical and energy eigenv...

We compare different solutions of the convection–diffusion–reaction problem with Danckwerts boundary conditions. Analytical solution is found, and method lines Crank–Nicholson are described, applied, compared for values Péclet Damköhler numbers. The eigenvalues eigenfunctions have been obtained all possible dimensionless parameters. And analytical expression concentration has calculated optimum...

We construct an expansion in generalized eigenfunctions for Schrödinger operators on metric graphs. We require rather minimal assumptions concerning the graph structure and the boundary conditions at the vertices.

We analyze the distribution of eigenvalues quantum-mechanical rotating harmonic oscillator by means Frobenius method. A suitable ansatz leads to a three-term recurrence relation for expansion coefficients. Truncation series yields some particular and eigenfunctions in exact analytical form. The former can be organized such way that one obtains information about whole spectrum model.