Exact Topological Soliton Solutions to the Strongly Perturbed Family of Sine-Gordon Type Equations

This paper uses the Ansatz method to solve for exact topological soliton solutions to sine-Gordon type equations. Single, double, and triple sine-Gordon and sine-cosine-Gordon equations are investigated along with dispersive and highly dispersive variations. After these solutions are found, strong perturbations are added to each equation and the new solutions are found. In solving both the perturbed and unperturbed sine-Gordon type equations, constraints are imposed on the parameters. The novel contributions of the authors are the soliton solutions to the strongly perturbed sine-Gordon equation and its variations. These results are important to the study of Josephson junctions, crystal dislocations, ultra-short optical pulses, relativistic field theory, and elementary particles.

Self-Consistent Field Theory of Ionization Collisions

A self-consistent field (SCF) theory for treating scattering systems was formulated previously and is extended here to the ionization process, in which the continuum orbitals are made square integrable by an amputation procedure. The method is applied to the electron-hydrogen scattering system in the zero angular momentum coupling model, and the differential cross section is compared with the recent results obtained by several other approaches. It is shown that the amputated continuum functions provide an effective projection of the scattering equation. SCF continuum functions generated in the present formalism are used to analyze the effective charge approximation.

Resonant Energy Transfer, with Creation of Hyper-Excited Atoms, and Molecular Auto-Ionization in a Cold Rydberg Gas

A cold Rydberg gas, with its atoms prepared initially all in the excited state |n0> , with n0 »1, contains an excessive amount of energy, and presumably is to relax by the Penning-type molecular auto-ionization (MAI), in which a portion of excess energy of one atom is given to another near-by atom and ionizing it. Its complementary process, the resonant energy transfer (RET), is discussed, in which the excess energy of one atom is used on another to form a hyper-excited atomic state |na> with na»n0. This process is always present, provided certain resonance energy conditions are satisfied. In this report, the n0 and density dependences of the RET rates are studied in detail, employing a simple model: 1) at low densities, the RET is mediated by the dipole-dipole coupling Vdd and its rates are generally much smaller than that of MAI, especially for small n0. But 2) as the density increases, our model shows that the rates become of comparable magnitude or even larger than the MAI rates. The Vdd is no longer adequate. We, then construct a semi-empirical potential to describe the RET process. 3) At high densities, we show that the atomic orbital of |na> overlaps with that of neighboring atoms, and the electron-electron potential becomes prominent, resulting in much higher rates.

Singular soliton solution and bifurcation analysis of Klein-Gordon equation with power law nonlinearity

In this paper, the Klein-Gordon equation （KGE） with power law nonlinearity will be considered. The bifurcation analysis as well as the ansatz method of integration will be applied to extract soliton and other wave solutions. In particular, the second approach to integration will lead to a singular soliton solution. However, the bifurcation analysis will reveal several other solutions that are of prime importance in relativistic quantum mechanics where this equation appears.