The initial value problem for the cubic nonlinear Klein–Gordon equation

We study the initial value problem for the cubic nonlinear Klein–Gordon equation

Periodic boundary value problem for nonlinear Sobolev-type equations

The large-time asymptotic behavior of solutions to the periodic boundary value problem for a nonlinear Sobolev-type equation is studied. In particular, the case where the initial perturbations are not small is considered. In this case, the large-time behavior of solutions is dichotomous.     

On a nonlinear equation with fractional derivative

We consider a nonlinear equation with fractional derivative in which the nonlinearity has the form of a linear combination of convective and nonconvective types. We prove the time-global existence of solutions of the Cauchy problem and find their asymptotics at large times uniformly with respect to the space variable. The proof method is based on a detailed investigation of the behavior of the Green function, which permits one to drop the restriction of smallness of the initial data in the case of a nonlinearity of special form.     

Modified Wave Operator for a System of Nonlinear Schrödinger Equations in 2d

We consider a system of nonlinear Schrödinger equations with quadratic nonlinearities in two space dimensions. We prove the existence of modified wave operators or wave operators under some mass conditions.     

Metastable intermolecular charge-transfer complexes with a pentavalent carbon atom

A novel type of metastable complexes of metal (such as Na) atoms with a super-fluorinated carbon molecule is investigated, with a carbon atom exhibiting a unique, pentavalent character. It is induced by the charge transfer from the alkali metal component, followed by a geometric compression of the ion pair system. Analysis of the electron-density distribution confirms the real chemical nature of the extra C-F bond. Structure and stability of the system are characterized ab initio, and a spectrum of electronic perturbations is considered. The ways of forming the systems are discussed, and the spectroscopic parameters are predicted, facilitating their detection in experiments.     

Nano-jewellery: C5Au12--a gold-plated diamond at molecular level

A mixed carbon-metal cluster is designed by combining the tetrahedral C(5) radical (with a central atom-the skeleton of the C(5)H(12) molecule) and the spherical Au(12) layer (the external atomic shell of the Au(13) cluster). The C(5)Au(12) cluster and its negative and positive ionic derivatives, C(5)Au(12)(+/-), are investigated ab initio (DFT) in terms of optimized structures and relative energies of a few spin-states, for the icosahedral-like and octahedral-like isomers. The cluster is predicted to be generally more stable in its octahedral shape (similar to C(5)H(12)) which prevails for the negative ion and may compete with the icosahedral shape for the neutral system and positive ion. Adiabatic ionization energies (AIE) and electron affinities (AEA) of C(5)Au(12), vertical electron-detachment (VDE) energies of C(5)Au(12)(-), and vertical ionization and electron-attachment energies (VIE, VEA) of C(5)Au(12) are calculated as well, and compared with those for the corresponding isomers of the Au(13) cluster. The AIE and VIE values are found to be close for the two systems, while the AEA and VDE values are significantly reduced for the radical-based species. A simple fragment-based model is proposed for the decomposition of the total interaction into carbon-gold and gold-gold components.