The quantization of the bosonic string in a general curved space-time has been the subject of intensive research for some time [1, 2, 3, 4]. Whereas the treatment by de Vega [1] relies on the canonical quantization, only few attempts of a path integral quantization have been made. Those attempts [3, 4] involved the semi-classical approximation, but despite their conceptual simplicity no attempt...

An eikonal expansion is developed in order to provide systematic corrections to the eikonal approximation through order 1/k, where k is the wave number. The expansion is applied to wave functions for the Klein-Gordon equation and for the Dirac equation with a Coulomb potential. Convergence is rapid at energies above about 250 MeV. Analytical results for the eikonal wave functions are obtained f...

A new transformation method is developed using the general sine-Gordon travelling wave reduction equation and a generalized transformation. With the aid of symbolic computation, this method can be used to seek more types of solutions of nonlinear differential equations, which include not only the known solutions derived by some known methods but new solutions. Here we choose the double sine-Gor...

The dynamics of two pairs of counter-propagating waves in two-component media is considered within the framework of two generally nonintegrable coupled Sine-Gordon equations. We consider the dynamics of weakly nonlinear wave packets, and using an asymptotic multiple-scales expansion we obtain a suite of evolution equations to describe energy exchange between the two components of the system. De...

The Material Point Method (MPM) developed by Sulsky and colleagues is currently being used to solve many challenging problems involving large deformations and/or fragmentations with some success. In order to understand the properties of this method, an analysis of the considerable computational properties of MPM is undertaken in the context of model problems from gas dynamics. The MPM method in...

The accuracy and effectiveness of various kinetic-energy functionals in providing total noninteracting kinetic energies, atomization kinetic energies, and equilibrium properties is evaluated. Employing converged Kohn-Sham densities, we assess various kinetic-energy functionals in a non-self-consistent manner. It is found that the gradient expansion, the Pearson-Gordon local truncation scheme, a...

We consider a one-dimensional continuum gas of pointlike positive and negative unit charges interacting via a logarithmic potential. The mapping onto a twodimensional boundary sine-Gordon field theory with zero bulk mass provides the full thermodynamics (density-fugacity relationship, specific heat, etc.) of the loggas in the whole stability range of inverse temperatures β < 1. An exact formula...

We consider the Klein-Gordon equation on a star-shaped network composed of n half-axes connected at their origins. We add a potential which is constant but different on each branch. The corresponding spatial operator is self-adjoint and we state explicit expressions for its resolvent and its resolution of the identity in terms of generalized eigenfunctions. This leads to a generalized Fourier t...