Nonlinear model of the DNA molecule

We study a simple nonlinear model that mimics many features of the DNA molecule, where the source of the nonlinearity is the hydrogen bonds between nucleotides. We find an asymptotic solution of the equations of motion in the limit of small amplitudes. For an arbitrary initial condition, however, the equations of motion have to be integrated numerically. In this case we find essentially two different regimes, one in which an initial pulselike disturbance is pinned, and another one in which it propagates along the chain. In this latter case, propagation is a linear effect, in which the nonlinearity plays little role.