Large-Amplitude Quasi-Solitons in Superfluid Films

Abstract

Nonlinear time evolution of the condensate wave function in superfluid films is studied on the basis of a Schrödinger equation, which incorporates van der Waals potential due to substrate in its fully nonlinear form, and a surface tension term. In the weak nonlinearity limit, our equation reduces to the ordinary (cubic) nonlinear Schrödinger equation for which exact soliton solutions are known. It is demonstrated by numerical analysis that even under strong nonlinearity , where our equation is far different from cubic Schrödinger equation, there exist quite stable composite “quasi-solitons" . These quasi-solitons are bound states of localized excitations of amplitude and phase of the condensate (superfluid thickness and superfluid velocity, in more physical terms). Thus the present work shows the persistence of the solitonic behavior of superfluid films in the fully nonlinear situation.