Enigma of probability amplitudes in Hamiltonian formulation of integrable semidiscrete nonlinear Schr\"{o}dinger systems
Oleksiy O. Vakhnenko

An attempt to find the probability-amplitude-based Hamiltonian representation for the symmetrical version of integrable semidiscrete multicomponent nonlinear Schr\"odinger system is made. Thus the on-cell locality of general point transformation in combination with the model multicomponentness is shown to contradict to the concept of canonical Hamiltonian representation in terms of probability amplitudes. Nevertheless the above concept can be realized in slightly adjusted semidiscrete multicomponent nonlinear Schr\"odinger system that preserves some physically valuable solutions of the original (either symmetric or asymmetric) integrable model. The advantages of adjusted Hamiltonian model for the analysis of real physical systems are formulated. Examples of longitudinal and lateral soliton dynamics on multichain tubular lattices subjected to uniform electric and magnetic fields are given.\\ PACS number(s): 63.20.Ry; 45.20.Jj; 02.30.Ik

© 2008 The American Physical Society.