Convergence of an approximate method for determining vibrational eigenpairs of an elastic solid containing an incompressible fluid is examined. The field variables are solid displacement and fluid pressure. We show that in suitable Sobolev spaces a variational formulation exists whose solution eigenvalues and eigenfunctions are identified with those of a compact operator. A nonconforming finite...

With a Rayleigh quotient formulation, a local minimax method is developed to solve a class of (iso-homogeneous) nonlinear eigenpair problems for multiple solutions in Banach spaces following their instability order. The algorithm is implemented to compute (weighted) eigenpairs of the p-Laplacian. Numerical eigenfunctions are illustrated by their graphics. Several interesting phenomena have been...

We construct efficient approximations for the eigenfunctions of non-selfadjoint Schrödinger operators in one dimension. The same ideas also apply to the study of resonances of self-adjoint Schrödinger operators which have dilation analytic potentials. In spite of the fact that such eigenfunctions can have surprisingly complicated structures with multiple local maxima, we show that a suitable ad...

The wall admittance of an arbitrarily shaped microstrip antenna is generally formulated. As examples, elliptical microstrip antennas with and without a circular slot are calculated. The wall admittance is determined by the spectral domain analysis in order to consider the effect of the dielectric substrate. The electromagnetic fields within the cavity are expanded in terms of the eigenfunctions...

We study the eigenpairs of a model Schrödinger operator with a quadratic potential and Neumann boundary conditions on a half-plane. The potential is degenerate in the sense that it reaches its minimum all along a line which makes the angle θ with the boundary of the half-plane. We show that the first eigenfunctions satisfy localization properties related to the distance to the minimum line of t...

in this paper, based on sinh-cosh method and sinh-gordon expansion method,families of solutions of (2+1)-dimensional breaking soliton equation are obtained.these solutions include jacobi elliptic function solution, soliton solution,trigonometric function solution.

A recurrent scheme for finding the quasiclassical solutions of the onedimensional equation got by the separation of variables from the Schrödinger equation in prolate spheroidal coordinates has been elaborated. By means of this scheme, WKB expansion quasiclassical two-Coulomb-centre wave functions at large distances between the fixed positive charges (nuclei) have been constructed for the entir...

A full-wave electromagnetic model is developed and verified for a waveguide transition consisting of slotted rectangular waveguides coupled to a strip line. This waveguide-based structure represents a portion of the planar spatial power combining amplifier array. The electromagnetic simulator is developed to analyze the stripline-to-slot transitions operating in a waveguidebased environment in ...

A consistent scheme is proposed for quantizing the potential amplitude in the Schrödinger equation in the caseof negative energies (lying in the discrete-spectrum domain). The properties of the eigenfunctionsφν(r) and eigenvalues ανcorresponding to zero, small, and large absolute values of energy E < 0 are analyzed. Expansion in the set {φν(r)} is used todevelop a regular pertur...