Coupled Schrödinger equations as a model of interchain torsional excitation transport in the DNA model

Physica Scripta. 2021. Vol. 96. No. 12. Article 125035.

Kovaleva M., Manevitch L. I.

In this report we consider two weakly coupled Schrödinger equations as a reduced model of interchain energy transport in the DNA double-helix torsional model. We employ a reduction of the Yakushevich-type model that considers the torsional dynamics of the DNA as effective chains of pendula. In previous works, only small amplitude excitations and stationary dynamics were investigated, whereas we focus on the nonstationary dynamics of the double helix. We consider the system to be a model of two weakly interacting DNA strands. Assuming that initially only one of the chains is excited in the form of a breather, we demonstrate the existence of an invariant that allows us to reduce the order of the problem and examine the system of the phase plane. The analysis demonstrates the utility of an analytical tool for predicting the periodic interchain excitation transitions of its localisation on one of the chains. The technique also takes into account the spreading of the excitations over time.

Keywords: связанные нелинейные уравнения Шредингера, energy transfer, энергообмен, DNA model, coupled nonlinear Schroedinger equations, модель ДНК