The inverse-spectral-transform method of solution is shown to be applicable to the physically interesting problem of the nonlinear Schrodinger equation with a general "potential" term, iq, +q +2[~q~-Fix)]q=0. The method determines the class of solutions that are symmetric or antisymmetric in x. This is done with the help of a modification of the Ablowitz-Kaup-Newell-Segur and Zakharov-Shabat (AKNS-ZS) formalism incorporating an xand t-dependent eigenvalue parameter g, together with a transformation of variables. In certain physical applications, F(x) describes the inhomogeneity of the medium in which nonlinear wave propagation occurs. The functions F(x) for which the equation is amenable to solution by our method are shown to fall into two classes, depending on whether or not g is explicitly t dependent. If it is, we show that F{x)must be a general quadratic function of x. An explicit solution q(x, t) is written down and interpreted for a parabolic potential barrier. If g is independent of t, we find that localized solutions with static envelopes can exist for certain other functional forms of F(x). Finally, we comment on the extension of the analysis to explicitly time-dependent potentials or inhomogeneities F(x,t).

We study the coherent nonlinear tunneling dynamics of a binary mixture of Bose-Einstein condensates in a double-well potential. We demonstrate the existence of a type of mode associated with the "swapping" of the two species in the two wells of the potential. In contrast to the symmetry-breaking macroscopic quantum self-trapping ͑MQST͒ solutions, the swapping modes correspond to the tunneling dynamics that preserves the symmetry of the double-well potential. As a consequence of two distinct types of broken-symmetry MQST phases where the two species localize in different potential wells or coexist in the same well, the corresponding symmetry-restoring swapping modes result in dynamics where the two species either avoid or chase each other. In view of the possibility to control the interaction between the species, the binary mixture offers a very robust system to observe these novel effects as well as the phenomena of Josephson oscillations and modes.

We study solitary wave propagation in the condensate of a system of hard-core bosons with nearest-neighbor interactions. For this strongly repulsive system, the evolution equation for the condensate order parameter of the system, obtained using spin coherent state averages is different from the usual Gross-Pitaevskii equation (GPE). The system is found to support two kinds of solitons when there is a particle-hole imbalance: a dark soliton that dies out as the velocity approaches the sound velocity, and a new type of soliton which brightens and persists all the way up to the sound velocity, transforming into a periodic wave train at supersonic speed. Analogous to the GPE soliton, the energy-momentum dispersion for both solitons is characterized by Lieb II modes.Strongly correlated quantum systems pose some of the most difficult challenges at the forefront of fundamental physics. Recent theoretical and experimental work in the field of BoseEinstein condensates (BEC) of atomic gases center around unveiling new phenomena that could lead to the understanding of various complexities of these systems. The possibility of tuning inter-atomic interactions via Feshbach resonances allows one to manipulate nature, and study realistic and tractable quantum many-body models. Among the various models, a system of impenetrable bosons known as the hard-core boson (HCB) gas, is a paradigm. It was analyzed exactly in one dimension by Girardeau [1]. It has also been used to explore quantum phase transitions[2] and transport characteristics of bosonic and spin-polarized fermionic atoms [3].In this paper, we study solitary wave propagation in a HCB system with nearest-neighbor (nn) interactions[4] to obtain deeper insight into beyond-GPE dynamics in quantum manybody systems. A soliton or solitary wave is a localized nonlinear excitation that travels with a constant speed, retaining its shape. Non-dispersive solitonic energy transport has been observed in a BEC [5]. These are the well known dark solitons that travel with speeds less than that of sound. Such particle-like transport is an active field with particular emphasis on unveiling many-body characteristics that cannot be described with the approximate description provided by the GPE. The existence of dark solitons have also been shown in a one-dimensional HCB gas using Fermi-Bose mapping [3], and in a generalized mean-field theory where the cubic nonlinearity of the GPE was replaced by a quintic term [6]. Solitons in similar quintic models were further investigated with a periodic potential [7], and also in the presence of a dipole-dipole interaction.[8] Additionally, various numerical investigations [9] have analyzed the quantum dynamics of dark solitons to study the effects of quantum fluctuations and quantum depletion in a Bose-Hubbard model.Our formulation, based on the equation for the BEC order parameter obtained using spin coherent state averages[11] differs considerably from earlier studies. In addition to not being restricted to one-dimension, the evolution equation for...

We use a spin-coherent representation to derive the spectrum of nonlinear excitations in a spin-S quantum ferromagnetic Heisenberg chain in the continuum limit. Quantum effects split the semiclassical spectrum into two branches-a lower branch of spin-wave-like, large-width solitary waves with negligible quantum corrections for all S, and an upper branch of particlelike, small-width solitary waves subject to significant quantum corrections for low S. The stability of these excitations is briefly discussed.

Lamb has identified a certain class of moving space curves with soliton equations. We show that there are two other classes of curve evolution that may be so identified. Hence three distinct classes of curve evolution are associated with a given integrable equation. The nonlinear Schrödinger equation is used to illustrate this explicitly.