Darboux Transformation of a Differential-Difference Equation and Its Explicit Solutions

The Darboux transformation of a differential-difference equation associated with a 3 × 3 matrix spectral problem is derived. As an application, explicit soliton solutions of the differential-difference equation are presented.     

Generation of radiation on yellow and infrared lines in sodium vapour excited to the 4P level

Generation of the radiation pulses on resonant (589 nm) as well as infrared (2210 nm and 1140 nm) lines was observed in sodium vapour excited by laser light tuned to the 3S–4P transition.     

On dynamic plane elasticity problems of 2D quasicrystals

In this Letter, the dynamic plane elasticity problems of 2D quasicrystals is considered. By use of the Fourier transform and matrix transformations the system is reduced to uncoupled ordinary differential equations. Fourier images of Green's functions for dynamic plane elasticity problems of 2D dodecagonal, pentagonal and decagonal quasicrystals are obtained explicitly by the suggested method.     

Rescaling Symmetry Flow of the Kadomtsev--Petviashvili Hierarchy

We present a new symmetry flow of the Kadomtsev-Petviashvili (KP) hierarchy, which origins from the rescaling of whole “multi-time“ valuables. This flow describes the deformation of solutions of the KP hierarchy with respect to a noncommutative parameter. It is shown that the introduced rescaling symmetry flow does not commute with the ordinary evolution flows of the KP hierarchy, but commutes with the evolution flows with respect to slow-variables.     

Ettore Majorana’s Course on Theoretical Physics: A Recent Discovery

We analyze in some detail the course that Ettore Majorana gave on theoretical physics at the University of Naples between January and March 1938, just prior to his mysterious disappearance. We discuss, in particular, the recently discovered Moreno Lecture Notes, in which all of Majorana’s lectures are recorded, six of which are not present in those that are preserved in the Domus Galilaeana in Pisa, Italy. Antonino Drago is a retired professor of history of physics at the University of Naples “Federico II.” Salvatore Esposito is a researcher on theoretical physics and history of physics at the University of Naples “Federico II.”     

Stability of Motion of a Nonholonomic System

Perturbation differential equations of motion of a general nonholonomic system subjected to the ideal nonholonomic constraints of Chetaev＇s type are established, and the equation of variation of energy is deduced by using the perturbation equations of the system. A criterion of the stability is obtained and an example is given to illustrate the application of the result.     

Transient and Stationary Simulations for a Quantum Hydrodynamic Model

The transient and stationary characteristics of a one-dimensional quantum hydrodynamic model are comparatively studied for semiconductor charge transport in a resonant tunnelling diode. When the bias is not small, our numerical results show a deviation of the asymptotic transient solutions from the stationary ones. A dynamic instability accounts for such deviation. The stationary quantum hydrodynamic model is therefore unsuitable in general for simulating quantum devices.     

Noncontinuous Solitary Wave Solutions for Double sine-Gordon Equation

Using the tanh method and a variable separated ordinary difference equation method to solve the double sineGordon equation, we derive some new exact travelling wave solutions, especially a new type of noncontinuous solitary wave solutions. These noncontinuous solitary wave solutions are verified by using the conservation law theory.     

Existence and Stability of Compact-Like Discrete Breather in Discrete One-Dimensional Monatomic Chains

Compact-like discrete breathers in discrete one-dimensional monatomic chains are investigated by discussing a generalized discrete one-dimensional monatomic model. It is proven that compact-like discrete breathers exist not only in soft Ф^4 potential but also in hard Ф^4 potential and K4 chains. The measurements of compact-like discrete breathers＇ core in soft and hard Ф^4 potential are determined by coupling parameter K4, while the measurements of compact-like discrete breathers＇ core in K4 chains are not related to coupling parameter K4. The stabilities of compact-like discrete breathers correlate closely to coupling parameter K4 and the boundary condition of lattice.     

Linearization of Systems of Nonlinear Diffusion Equations

We investigate the linearization of systems of n-component nonlinear diffusion equations; such systems have physical applications in soil science, mathematical biology and invariant curve flows. Equivalence transformations of their auxiliary systems are used to identify the systems that can be linearized. We also provide several examples of systems with two-component equations, and show how to linearize them by nonlocal mappings.