Complex Ginzburg-Landau equation in the modified Peyrard-Bishop-Dauxois model

The modified Peyrard-Bishop-Dauxois model can be generalized, and through the semidiscrete approximation, we show that the dynamics of motion, associated with the DNA breather, is governed by the complex quintic Ginzburg-Landau equation. We discuss the impact of quintic term in the breather formations. The linear study of the plane wave solution has been investigated, in particular, it is shown that the instability diagram is steeply modified by the increase of the quintic parameter. One obtains wave pattern formations. Thereafter the wave patterns presented are in very robust form, which from a biological point of view, constitute opening states, observed during the vital events namely recombination-repair. These emerged structures can be strongly controlled by the quintic nonlinear parameter. The introduction of the quintic nonlinearity induces the new generations of modulated waves and also provokes the increasing of the waves amplitude. Our numerical study proves the validity of the analytical investigation where we observe the birth of wave excitations spreading with irregular features due to the increase in quintic parameter. This also confirms that the wave number falls well in the disturbance domains.

Automated summary

This article investigates the dynamics of DNA breather motion using the modified Peyrard-Bishop-Dauxois model, and shows that it is governed by the complex quintic Ginzburg-Landau equation. The impact of the quintic term on breather formations and the characteristics of wave excitations generated by the introduction of the quintic nonlinearity are discussed.