Structure of soliton bound states in the parametrically driven and damped nonlinear systems

English

[en] Structure of soliton bound states in the parametrically driven and damped nonlinear systems

Bogdan, M.M.[B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine]

Charkina, Oksana[University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS) >]

[en] Static soliton bound states in nonlinear systems are investigated analytically and numerically in the framework of the parametrically driven and damped nonlinear SchrÃ¶dinger equation. We find that the ordinary differential equations, which determine bound soliton solutions, can be transformed into the form resembling the SchrÃ¶dinger-like equations for eigenfunctions with fixed eigenvalues. We assume that a nonlinear part of the equations is close to the reflectionless potential well occurring in the scattering problem associated with the integrable equations. We show that symmetric two-hump soliton solution is quite well described analytically by the three-soliton formula with the fixed soliton parameters, depending on the strength of parametric pumping and the dissipation constant.