Transverse and longitudinal dynamics of nonlinear intramolecular excitations on multileg ladder lattices

A model of nonlinear intramolecular excitations on a multileg ladder lattice integrable by the inverse scattering transform is elaborated. The principal question of how to include the interchain linear coupling between excitations in the inverse scattering scheme is solved, and a detailed outline of the inverse scattering technique transforming the initially nonlinear problem into a linear one is given. The model permits a number of physically interesting applications related to striplike and bunchlike biological and condensed matter systems and in its partially continuous form to arrays of linearly and nonlinearly coupled optical fibers. The soliton dynamics across and along the chains for the cases of two-leg and three-leg ladder lattices is analyzed. The effect of an external magnetic field on the transverse dynamics of charged excitations on a three-leg ladder lattice with triangular cross section is studied and circular traveling as well as standing modes supporting the oscillating redistribution of soliton density between the chains are described. From the physical point of view it is reasonable to treat all transverse modes caused by interchain linear couplings as breathing modes, insofar as they correspond to the intrinsic degrees of freedom of a spatially constricted nonlinear wave packet moving uniformly as a whole along the chains.