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Introduction

This site is devoted to the presentation of the dynamics of discrete breathes (DB) - spatial localized and time-periodic object. They exist in different systems and were observed numerically and experimentally. If you are not familiar with such objects, it is better to read some papers before [1,2,3].

The system under consideration is 1D Hamiltonian lattice

$\displaystyle H=\sum\limits_n\frac{1}{2}\dot{x}_n+V(x_n)+W(x_n-x_{n-1})$     (1)

where on-site potential is
$\displaystyle V(z)=\left\{
\begin{array}{l}
\frac{V_2}{2}z^2+\frac{V_3}{3}z^3+\...
...4}{4}z^4\\
V_c(1-\cos z)\\
\frac{V_m}{2}(1-{\rm e}^{-z})^2
\end{array}\right.$     (2)

and coupling potential
$\displaystyle W(y)=\frac{W_2}{2}y^2+\frac{W_3}{3}y^3+\frac{W_4}{4}y^4$     (3)

The equations of the motion are
$\displaystyle \ddot{x}_n=-V^{\prime}(x_n)+W^{\prime}(x_{n+1}-x_n)-W^{\prime}(x_n-x_{n-1})$     (4)

The spectrum of the small amplitude excitations is
$\displaystyle \omega_q^2=V^{\prime\prime}(0)+4W^{\prime\prime}(0)\sin^2(\frac{q}{2})$     (5)



Andrey Miroshnchenko 2003-01-15