Dynamical Barrier for the Formation of Solitary Waves in Discrete Lattices

Details Dynamical Barrier for the Formation of Solitary Waves in Discrete Lattices Dynamical Barrier for the Formation of Solitary Waves in Discrete Lattices

2007-11-12

arxiv.org/abs/0711.1895v1

Nonlinear Sciences

Pattern Formation and Solitons

9 pages, 3 figures, Phys. Lett. A (in press)

Scientific paper

10.1016/j.physleta.2007.11.029

We consider the problem of the existence of a dynamical barrier of ``mass'' that needs to be excited on a lattice site to lead to the formation and subsequent persistence of localized modes for a nonlinear Schrodinger lattice. We contrast the existence of a dynamical barrier with its absence in the static theory of localized modes in one spatial dimension. We suggest an energetic criterion that provides a sufficient, but not necessary, condition on the amplitude of a single-site initial condition required to form a solitary wave. We show that this effect is not one-dimensional by considering its two-dimensional analog. The existence of a sufficient condition for the excitation of localized modes in the non-integrable, discrete, nonlinear Schrodinger equation is compared to the dynamics of excitations in the integrable, both discrete and continuum, version of the nonlinear Schrodinger equation.

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