Numerically exact mobile breathers in Peyrard-Bishop DNA model

Discrete breathers are spatially localized, time periodic oscillations. They appear in discrete nonlinear systems, particularly in the quasi-linear molecular chains. An interesting example of such objects is the Peyrard-Bishop model of deoxyribonucleic acid molecule (DNA) and its modifications. In the models, discrete breathers precede denaturation bubbles (the regions of separation of complementary chains in the course of the DNA melting). Under certain conditions, such localized oscillations can move and they are known as mobile breathers. There is a systematic method for finding solutions of nonlinear discrete systems in the form of approximate mobile breathers. Approximate mobile breathers have quite a long lifetime, but they move slowly losing energy due to the emission of phonons. However, in nonlinear discrete lattices numerical studies show the existence of so-called numerically exact mobile breathers, moving without loss of energy and changing its shape. The present article deals with these numerically exact mobile breathers in the Peyrard-Bishop model of DNA. A method for finding numerically exact mobile breather is considered. After some periods, these solutions repeat the same profile but displaced by several lattice sites. Numerically exact mobile breather can be obtained only at certain values of the interparticle interaction describing stacking interaction of DNA.