Nonlinear charge and energy transport in anharmonic quasi-two-dimensional systems.

We study the localized states of an extra electron in an anisotropic quasi-two-dimensional system in which the electron-lattice interaction and the anharmonicity of the lattice vibrations are dominant in one direction. This model describes layers of polydiacetylene or other polymer chains, beta sheets of polypeptides, multilevel microstructures of conjugated polymers, and other low-dimensional systems. It is shown that for appropriate parameter values of the system an extra electron can excite a soliton-like mobile wave of the lattice deformation, within which it can get self-trapped.

Turing Instabilities and Rotating Spiral Waves in Glycolytic Processes.

We study single-frequency oscillations and pattern formation in the glycolytic process modeled by a reduction in the well-known Sel'kov's equations (Sel'kov in Eur J Biochem 4:79, 1968), which describe, in the whole cell, the phosphofructokinase enzyme reaction. By using averaging theory, we establish the existence conditions for limit cycles and their limiting average radius in the kinetic reaction equations. We analytically establish conditions on the model parameters for the appearance of unstable nonlinear modes seeding the formation of two-dimensional patterns in the form of classical spots and stripes.

Multi-hump bright and dark solitons for the Schrödinger-Korteweg-de Vries coupled system.

The Hirota bilinear method is extended to find one- and two-hump exact bright and dark soliton solutions to a coupled system between the linear Schrödinger and Korteweg-de Vries (KdV) equations arising in the energy transfer problem along a cubic anharmonic crystal medium. The bilinear form associated to this system is found by imitating the well known bilinearizing transformations used in the standard nonlinear Schrödinger (NLS) and KdV equations. Proper finite exponential expansions in the transformed variables allow one to exhibit multihump soliton solutions as single entities resulting from the adjustment of appropriate dispersion relations between the wave parameters describing the profiles.

Effect of hydrogen bond anharmonicity on supersonic discrete Davydov soliton propagation.

We consider the propagation of energy along a protein chain in the Davydov approximation. We study the fully discrete Davydov equations including the anharmonic corrections in the hydrogen bond potential and find approximate variational solutions. We show analytically that for the harmonic interaction of the hydrogen bonds of the Davydov model the waves travel with velocities less than half the sound velocity for the relevant biological parameters.